Class 9 Coordinate Geometry
|
|
- Crystal Houston
- 5 years ago
- Views:
Transcription
1 ID : in-9-coordinate-geometry [1] Class 9 Coordinate Geometry For more such worksheets visit Answer the questions (1) Find the coordinates of the point shown in the picture. (2) Find the distance of the point (-6, -2) from y-axis. (3) Which of the points W(6, 0), X(0, 16), Y(7, 0) and Z(0, -15) lie on the x-axis? (4) Find the coordinate of the point whose abscissa is 9 and lies on x-axis. (5) Vinayak and Radha deposit some amount in a joint bank account such that total balance remains 800. If amount deposited by Vinayak and Radha are plotted as a linear graph on xy plane, find the area between this graph and the coordinate axis. (6) Find the resultant shape obtained by connecting the points (-30, -20), (-30, 5), (-20, 5) and (-20, -20).
2 (7) Find the coordinates of the point shown in the picture. ID : in-9-coordinate-geometry [2]
3 (8) If coordinates of the point shown in the picture are (p+25, p+30), find the value of p. ID : in-9-coordinate-geometry [3] (9) Find the coordinates of the point which lies on the y-axis at a distance of 9 units from origin in the negative direction of y-axis. (10) Point (-8, 1) lies in which quadrant? Choose correct answer(s) from the given choices (11) A point whose abscissa and ordinate are both negative will lie in the: a. Fourth quadrant b. First quadrant c. Third quadrant d. Second quadrant (12) Signs of the abscissa and ordinate of a point in the third quadrant are: a. -, + b. +, + c. +, - d. -, - (13) Two distinct points in a plane determine line. a. three b. one unique c. two d. infinite (14) The point in which the abscissa and the ordinate have same sign will lie in: a. First or Third quadrant b. Second or Fourth quadrant c. Third or Fourth quadrant d. Second or Third quadrant
4 ID : in-9-coordinate-geometry [4] (15) Two distinct in a plane can not have more than one point in common. a. both lines and points b. planes c. lines d. points 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at
5 Answers ID : in-9-coordinate-geometry [5] (1) (-20, 20) In order to find the coordinates of the point shown in the picture, let us draw a horizontal and a vertical line that connects this point to the y-axis and x-axis respectively. We can see that the vertical line intersects the x-axis at -20. Therefore, the x-coordinate of the point is -20. Similarly, the horizontal line intersects the y-axis at 20. Therefore, the y-coordinate of the point is 20. Step 4 Hence, the coordinates of the given point are (-20, 20).
6 (2) 6 ID : in-9-coordinate-geometry [6] The simplest way to solve it is to remember that the abscissa is the position "on" the x-axis, and the ordinate is the position "on" the y-axis. This means that the first value is the distance of the point from the y-axis, and the ordinate is the distance of the point from the x-axis. Also remember to remove the negative sign as the distance is always positive. We have to find the distance of the given point (-6, -2) from y-axis, which will be equal to the abscissa of the point (ignoring the negative sign),i.e., 6. (3) Y and W We know that a point lying on the x-axis will have the ordinate as 0 and a point lying on the y-axis will have the abscissa as 0. We can see that out of all the points Y and W have the ordinate zero, which means points Y and W will lie on the x-axis. (4) (9,0) The first value x, of coordinates of any point (x, y) is called the abscissa, and the second value y is called the ordinate. Now, we know that if a point lies on the x-axis then its ordinate is 0. In the given question, since the point lies on x-axis and the value of its abscissa is 9, the coordinates of the point will be (9,0).
7 (5) ID : in-9-coordinate-geometry [7] Let the amount deposited by Vinayak be x and by Radha be y. Since the balance remains 800, the relation between x and y will be given by x + y = 800. We know that the area of a triangle is equal to half the product of base and the height. Step 4 The area of the given triangle will be equal to: = sq units.
8 (6) Rectangle ID : in-9-coordinate-geometry [8] Let us plot the given points on a graph paper and join them as shown below: Now, we notice the following: 1. Opposite sides are equal and parallel to each other. 2. All angles are equal and are right angles. These are the properties of a Rectangle. Therefore, the shape obtained on joining these points is a Rectangle.
9 (7) (-1, -3) ID : in-9-coordinate-geometry [9] In order to find the coordinates of the point shown in the picture, let us draw a horizontal and a vertical line which connect this point to the y-axis and x-axis respectively. We can see that the vertical line intersects the x-axis at -1. Therefore, the abscissa of the point is - 1. Similarly, the horizontal line intersects the y-axis at -3. Therefore, the ordinate of the point is -3. Step 4 Hence, the coordinates of the given point are (-1, -3).
10 (8) 5 ID : in-9-coordinate-geometry [10] From observation we see that the point defined is (30,35). It is given that, 30 = p + 25 and 35 = p + 30 or, p = 5 From either of these equations we can see that p = 5. (9) (0, -9) Since the given point lies on the y axis, its abscissa will be equal to zero. The distance of the point from the origin is 9 units in the negative direction. This means that the ordinate of the point will be -9. From above two steps, we can say that the point is (0, -9).
11 (10) Second quadrant ID : in-9-coordinate-geometry [11] For plotting a point (x, y) on the graph, we have to keep in mind the following points: If both the numbers are positive i.e. (x,y), then the point lies in the first quadrant. If the first number is negative, and the second number is positive i.e. (-x,y), it lies in the second quadrant. If both the numbers are negative (-x,-y), it lies in the third quadrant. If the first number is positive and the second number is negative (x,-y), it lies in the fourth quadrant. We can see that for the given point, x is less than zero and y is greater than zero. Hence, the point will lie in the Second quadrant.
12 (11) c. Third quadrant ID : in-9-coordinate-geometry [12] There is a very simple mental map for this as shown below: We need to go in the anticlockwise direction for this. If both the numbers are positive (x,y), then the point lies in the first quadrant. If the first number is negative, and the second is positive (-x,y), it lies in the second quadrant. Step 4 If both numbers are negative (-x,-y), it lies in the third quadrant. Step 5 If the first is positive and the second is negative (x,-y), it lies in the fourth quadrant. Step 6 Here both values are negative, therefore it will lie in the Third quadrant.
13 (12) d. -, - ID : in-9-coordinate-geometry [13] The key to solving such questions is to build a mental map of the quadrants. The quadrants get decided based on the following points: i. When both abscissa and ordinate are positive i.e. (x,y), then the point lies in the first quadrant. (The positioning of next quadrants will be done in anticlockwise direction.) ii. When abscissa is negative and ordinate is positive i.e. (-x,y), it lies in quadrant two. iii. When abscissa and ordinate both are negative i.e. (-x,-y), it lies in quadrant three. iv. When abscissa is positive and ordinate is negative i.e. (x,-y), it lies in quadrant four. (13) b. one unique Following figure shows a line, that is drawn through two distinct points A and B. If we try to draw another line, it will not go through both A and B. Therefore, two distinct points in a plane determine one unique line.
14 (14) a. First or Third quadrant ID : in-9-coordinate-geometry [14] There is a very simple mental map for this. In the first quadrant, both the abscissa and ordinate (x,y) are positive. In the second quadrant, the abscissa is negative, and the ordinate is positive (-x,y). Step 4 In the third quadrant, both the numbers are negative (-x,-y). Step 5 In the fourth quadrant, the abscissa is positive and the ordinate is negative (x,-y). Step 6 Based on this, we find the answer to the question is First or Third quadrant. (15) c. lines Following figure shows the lines AB and CD, intersected at the point E. From the given figure it is clear that, the two distinct lines can intersect at a single point only and hence, we can say that the two distinct lines in a plane can not have more than one point in common.
CO-ORDINATE GEOMETRY CHAPTER 3. Points to Remember :
CHAPTER Points to Remember : CO-ORDINATE GEOMETRY 1. Coordinate axes : Two mutually perpendicular lines X OX and YOY known as x-axis and y-axis respectively, constitutes to form a co-ordinate axes system.
More information10 GRAPHING LINEAR EQUATIONS
0 GRAPHING LINEAR EQUATIONS We now expand our discussion of the single-variable equation to the linear equation in two variables, x and y. Some examples of linear equations are x+ y = 0, y = 3 x, x= 4,
More informationChapter 9 Linear equations/graphing. 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane
Chapter 9 Linear equations/graphing 1) Be able to graph points on coordinate plane 2) Determine the quadrant for a point on coordinate plane Rectangular Coordinate System Quadrant II (-,+) y-axis Quadrant
More informationClass 5 Geometry O B A C. Answer the questions. For more such worksheets visit
ID : in-5-geometry [1] Class 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) The set square is in the shape of. (2) Identify the semicircle that contains 'C'. A C O B
More informationChapter 2: Functions and Graphs Lesson Index & Summary
Section 1: Relations and Graphs Cartesian coordinates Screen 2 Coordinate plane Screen 2 Domain of relation Screen 3 Graph of a relation Screen 3 Linear equation Screen 6 Ordered pairs Screen 1 Origin
More informationE. Slope-Intercept Form and Direct Variation (pp )
and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the
More information4.4 Slope and Graphs of Linear Equations. Copyright Cengage Learning. All rights reserved.
4.4 Slope and Graphs of Linear Equations Copyright Cengage Learning. All rights reserved. 1 What You Will Learn Determine the slope of a line through two points Write linear equations in slope-intercept
More informationACT Coordinate Geometry Review
ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this
More informationActivity 11 OBJECTIVE. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry box, pen/pencil.
Activity 11 OBJECTIVE To find the values of abscissae and ordinates of various points given in a cartesian plane. MATERIAL REQUIRED Cardboard, white paper, graph paper with various given points, geometry
More informationPlotting Points in 2-dimensions. Graphing 2 variable equations. Stuff About Lines
Plotting Points in 2-dimensions Graphing 2 variable equations Stuff About Lines Plotting Points in 2-dimensions Plotting Points: 2-dimension Setup of the Cartesian Coordinate System: Draw 2 number lines:
More informationSIMILARLY IN CASE OF TINY OBJECTS DIMENSIONS MUST BE INCREASED FOR ABOVE PURPOSE. HENCE THIS SCALE IS CALLED ENLARGING SCALE. FOR FULL SIZE SCALE R.
DIMENSIONS OF LARGE OBJECTS MUST BE REDUCED TO ACCOMMODATE ON STANDARD SIZE DRAWING SHEET.THIS REDUCTION CREATES A SCALE OF THAT REDUCTION RATIO, WHICH IS GENERALLY A FRACTION.. SUCH A SCALE IS CALLED
More informationPart I: Bell Work When solving an inequality, when would you flip the inequality sign?
Algebra 135 Seminar Lesson 55 Part I: Bell Work When solving an inequality, when would you flip the inequality sign? Part II: Mini-Lesson Review for Ch 6 Test Give a review lesson for the Chapter 6 test.
More informationTable of Contents Problem Solving with the Coordinate Plane
GRADE 5 UNIT 6 Table of Contents Problem Solving with the Coordinate Plane Lessons Topic 1: Coordinate Systems 1-6 Lesson 1: Construct a coordinate system on a line. Lesson 2: Construct a coordinate system
More informationMath Labs. Activity 1: Rectangles and Rectangular Prisms Using Coordinates. Procedure
Math Labs Activity 1: Rectangles and Rectangular Prisms Using Coordinates Problem Statement Use the Cartesian coordinate system to draw rectangle ABCD. Use an x-y-z coordinate system to draw a rectangular
More informationSect Linear Equations in Two Variables
99 Concept # Sect. - Linear Equations in Two Variables Solutions to Linear Equations in Two Variables In this chapter, we will examine linear equations involving two variables. Such equations have an infinite
More informationEconomics 101 Spring 2017 Answers to Homework #1 Due Thursday, Feburary 9, 2017
Economics 101 Spring 2017 Answers to Homework #1 Due Thursday, Feburary 9, 2017 Directions: The homework will be collected in a box before the large lecture. Please place your name, TA name and section
More informationClass 8 Cubes and Cube Root
ID : in-8-cubes-and-cube-root [1] Class 8 Cubes and Cube Root For more such worksheets visit www.edugain.com Answer the questions (1) Find the value of A if (2) If you subtract a number x from 15 times
More informationCC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now:
CC Geometry H Aim #3: How do we rotate points 90 degrees on the coordinate plane? Do Now: 1. a. Write the equation of the line that has a slope of m = and passes through the point (0, 3). Graph this equation
More informationStudents use absolute value to determine distance between integers on the coordinate plane in order to find side lengths of polygons.
Student Outcomes Students use absolute value to determine distance between integers on the coordinate plane in order to find side lengths of polygons. Lesson Notes Students build on their work in Module
More informationThe Cartesian Coordinate System
The Cartesian Coordinate System The xy-plane Although a familiarity with the xy-plane, or Cartesian coordinate system, is expected, this worksheet will provide a brief review. The Cartesian coordinate
More informationSet No - 1 I B. Tech I Semester Regular/Supplementary Examinations Jan./Feb ENGINEERING DRAWING (EEE)
Set No - 1 I B. Tech I Semester Regular/Supplementary Examinations Jan./Feb. - 2015 ENGINEERING DRAWING Time: 3 hours (EEE) Question Paper Consists of Part-A and Part-B Answering the question in Part-A
More informationINTRODUCTION TO GRAPHS
UNIT 12 INTRODUCTION TO GRAPHS (A) Main Concepts and Results Graphical representation of data is easier to understand. A bar graph, a pie chart and histogram are graphical representations of data. A line
More informationIn this section, we find equations for straight lines lying in a coordinate plane.
2.4 Lines Lines In this section, we find equations for straight lines lying in a coordinate plane. The equations will depend on how the line is inclined. So, we begin by discussing the concept of slope.
More informationMathematics Success Grade 6
T428 Mathematics Success Grade 6 [OBJECTIVE] The students will plot ordered pairs containing rational values to identify vertical and horizontal lengths between two points in order to solve real-world
More informationTutor-USA.com Worksheet
Tutor-USA.com Worksheet Geometry Points, Lines, and Planes ame: Date: Y C G E H X A B F D 1) Name the two planes in the above figure. 2) List the points labeled in the above figure. Classify each statement
More informationDiscussion 8 Solution Thursday, February 10th. Consider the function f(x, y) := y 2 x 2.
Discussion 8 Solution Thursday, February 10th. 1. Consider the function f(x, y) := y 2 x 2. (a) This function is a mapping from R n to R m. Determine the values of n and m. The value of n is 2 corresponding
More informationISOMETRIC PROJECTION. Contents. Isometric Scale. Construction of Isometric Scale. Methods to draw isometric projections/isometric views
ISOMETRIC PROJECTION Contents Introduction Principle of Isometric Projection Isometric Scale Construction of Isometric Scale Isometric View (Isometric Drawings) Methods to draw isometric projections/isometric
More informationCH 54 SPECIAL LINES. Ch 54 Special Lines. Introduction
479 CH 54 SPECIAL LINES Introduction Y ou may have noticed that all the lines we ve seen so far in this course have had slopes that were either positive or negative. You may also have observed that every
More informationClass 10 Trigonometry
ID : in-10-trigonometry [1] Class 10 Trigonometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) An equilateral triangle width side of length 18 3 cm is inscribed in a circle.
More informationSection 3.5. Equations of Lines
Section 3.5 Equations of Lines Learning objectives Use slope-intercept form to write an equation of a line Use slope-intercept form to graph a linear equation Use the point-slope form to find an equation
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More information2.4 Translating Sine and Cosine Functions
www.ck1.org Chapter. Graphing Trigonometric Functions.4 Translating Sine and Cosine Functions Learning Objectives Translate sine and cosine functions vertically and horizontally. Identify the vertical
More information3-5 Slopes of Lines. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the value of m. 1. 2. 3. 4. undefined 0 Objectives Find the slope of a line. Use slopes to identify parallel and perpendicular
More informationActual testimonials from people that have used the survival guide:
Algebra 1A Unit: Coordinate Plane Assignment Sheet Name: Period: # 1.) Page 206 #1 6 2.) Page 206 #10 26 all 3.) Worksheet (SIF/Standard) 4.) Worksheet (SIF/Standard) 5.) Worksheet (SIF/Standard) 6.) Worksheet
More informationYou could identify a point on the graph of a function as (x,y) or (x, f(x)). You may have only one function value for each x number.
Function Before we review exponential and logarithmic functions, let's review the definition of a function and the graph of a function. A function is just a rule. The rule links one number to a second
More informationChapter 3 Linear Equations in Two Variables
Chapter Linear Equations in Two Variables. Check Points. 6. x y x ( x, y) y ( ) 6, 6 y ( ), 0 y (0) 0, y () 0,0 y (),. E(, ) F(,0) G (6,0). a. xy 9 ( ) 9 69 9 9, true (, ) is a solution. b. xy 9 () 9 99
More informationOptimization Exploration: The Inscribed Rectangle. Learning Objectives: Materials:
Optimization Exploration: The Inscribed Rectangle Lesson Information Written by Jonathan Schweig and Shira Sand Subject: Pre-Calculus Calculus Algebra Topic: Functions Overview: Students will explore some
More informationMATH Exam 2 Solutions November 16, 2015
MATH 1.54 Exam Solutions November 16, 15 1. Suppose f(x, y) is a differentiable function such that it and its derivatives take on the following values: (x, y) f(x, y) f x (x, y) f y (x, y) f xx (x, y)
More informationWe are going to begin a study of beadwork. You will be able to create beadwork on the computer using the culturally situated design tools.
Bead Loom Questions We are going to begin a study of beadwork. You will be able to create beadwork on the computer using the culturally situated design tools. Read the first page and then click on continue
More informationLesson 10.1 Skills Practice
Lesson 10.1 Skills Practice Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular lines parallel
More informationChapter 9. Conic Sections and Analytic Geometry. 9.1 The Ellipse. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 9 Conic Sections and Analytic Geometry 9.1 The Ellipse Copyright 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Graph ellipses centered at the origin. Write equations of ellipses in standard
More informationRAKESH JALLA B.Tech. (ME), M.Tech. (CAD/CAM) Assistant Professor, Department Of Mechanical Engineering, CMR Institute of Technology. CONICS Curves Definition: It is defined as the locus of point P moving
More informationSecond Semester Session Shri Ramdeobaba College of Engineering & Management, Nagpur. Department of Mechanical Engineering
Second Semester Session- 2017-18 Shri Ramdeobaba College of Engineering & Management, Nagpur. Department of Mechanical Engineering Engineering Drawing Practical Problem Sheet Sheet No.:- 1. Scales and
More informationWarm-Up. Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011.
Warm-Up Complete the second homework worksheet (the one you didn t do yesterday). Please begin working on FBF010 and FBF011. You have 20 minutes at the beginning of class to work on these three tasks.
More informationLesson 6.1 Linear Equation Review
Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can
More informationCH 21 2-SPACE. Ch 21 2-Space. y-axis (vertical) x-axis. Introduction
197 CH 21 2-SPACE Introduction S omeone once said A picture is worth a thousand words. This is especially true in math, where many ideas are very abstract. The French mathematician-philosopher René Descartes
More informationMathematics 205 HWK 19b Solutions Section 16.2 p750. (x 2 y) dy dx. 2x 2 3
Mathematics 5 HWK 9b Solutions Section 6. p75 Problem, 6., p75. Evaluate (x y) dy dx. Solution. (x y) dy dx x ( ) y dy dx [ x x dx ] [ ] y x dx Problem 9, 6., p75. For the region as shown, write f da as
More informationChapter 6: Linear Relations
Chapter 6: Linear Relations Section 6. Chapter 6: Linear Relations Section 6.: Slope of a Line Terminolog: Slope: The steepness of a line. Also known as the Rate of Change. Slope = Rise: The change in
More informationRECTANGULAR COORDINATE SYSTEM
RECTANGULAR COORDINATE SYSTEM Quadrant II (x0) 5 4 Quadrant I (x > 0, y>0) ORDERED PAIR: The first number in the ordered pair is the x- coordinate (aka abscissa) and the second number in the ordered
More informationENGINEERING DRAWING
Subject Code: R13109/R13 Set No - 1 I B. Tech I Semester Regular/Supplementary Examinations Jan./Feb. - 2015 ENGINEERING DRAWING (Common to ECE, EIE, Bio-Tech, EComE, Agri.E) Time: 3 hours Max. Marks:
More informationPROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES
PROPORTIONAL VERSUS NONPROPORTIONAL RELATIONSHIPS NOTES Proportional means that if x is changed, then y is changed in the same proportion. This relationship can be expressed by a proportional/linear function
More informationClass VIII Chapter 15 Introduction to Graphs Maths
Exercise 15.1 Question 1: The following graph shows the temperature of a patient in a hospital, recorded every hour. (a) What was the patient s temperature at 1 p.m.? (b) When was the patient s temperature
More informationUnderstanding Projection Systems
Understanding Projection Systems A Point: A point has no dimensions, a theoretical location that has neither length, width nor height. A point shows an exact location in space. It is important to understand
More informationMath 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004
Math 1023 College Algebra Worksheet 1 Name: Prof. Paul Bailey September 22, 2004 Every vertical line can be expressed by a unique equation of the form x = c, where c is a constant. Such lines have undefined
More informationGrade 6 Natural and Whole Numbers
ID : ae-6-natural-and-whole-numbers [1] Grade 6 Natural and Whole Numbers For more such worksheets visit www.edugain.com Answer the questions (1) Find the successor of the given number: 4614143 (2) If
More informationChapter 3, Part 1: Intro to the Trigonometric Functions
Haberman MTH 11 Section I: The Trigonometric Functions Chapter 3, Part 1: Intro to the Trigonometric Functions In Example 4 in Section I: Chapter, we observed that a circle rotating about its center (i.e.,
More informationConnected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)
Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change
More informationLearning Log Title: CHAPTER 2: ARITHMETIC STRATEGIES AND AREA. Date: Lesson: Chapter 2: Arithmetic Strategies and Area
Chapter 2: Arithmetic Strategies and Area CHAPTER 2: ARITHMETIC STRATEGIES AND AREA Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 2: Arithmetic Strategies and Area Date: Lesson:
More informationCartesian Coordinate System. Student Instruction S-23
QuickView Design a 6 x 6 grid based on the Cartesian coordinates. Roll two dice to determine the coordinate points on the grid for a specific quadrant. Use the T-Bot II to place a foam block onto the rolled
More informationGraphing Lines with a Table
Graphing Lines with a Table Select (or use pre-selected) values for x Substitute those x values in the equation and solve for y Graph the x and y values as ordered pairs Connect points with a line Graph
More information4.4 Equations of Parallel and Perpendicular
www.ck12.org Chapter 4. Determining Linear Equations 4.4 Equations of Parallel and Perpendicular Lines Learning Objectives Determine whether lines are parallel or perpendicular. Write equations of perpendicular
More informationChapter 4 ORTHOGRAPHIC PROJECTION
Chapter 4 ORTHOGRAPHIC PROJECTION 4.1 INTRODUCTION We, the human beings are gifted with power to think. The thoughts are to be shared. You will appreciate that different ways and means are available to
More informationLesson 7 Slope-Intercept Formula
Lesson 7 Slope-Intercept Formula Terms Two new words that describe what we've been doing in graphing lines are slope and intercept. The slope is referred to as "m" (a mountain has slope and starts with
More informationPage 21 GRAPHING OBJECTIVES:
Page 21 GRAPHING OBJECTIVES: 1. To learn how to present data in graphical form manually (paper-and-pencil) and using computer software. 2. To learn how to interpret graphical data by, a. determining the
More informationName Period Date LINEAR FUNCTIONS STUDENT PACKET 5: INTRODUCTION TO LINEAR FUNCTIONS
Name Period Date LF5.1 Slope-Intercept Form Graph lines. Interpret the slope of the graph of a line. Find equations of lines. Use similar triangles to explain why the slope m is the same between any two
More informationGeometry. Practice Pack
Geometry Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Lines and Angles Practice 1.1 What Is Geometry?........................ 1 Practice 1.2 What Is Geometry?........................ 2 Practice
More informationMaxima and Minima. Terminology note: Do not confuse the maximum f(a, b) (a number) with the point (a, b) where the maximum occurs.
10-11-2010 HW: 14.7: 1,5,7,13,29,33,39,51,55 Maxima and Minima In this very important chapter, we describe how to use the tools of calculus to locate the maxima and minima of a function of two variables.
More informationAnalytical geometry. Multiple choice questions
Analytical geometry Multiple choice questions 1. Temperature readings on any given day in Québec can vary greatly. The temperatures for a fall day in Montreal were recorded over a 10-hour interval. The
More informationLesson 10. Unit 2. Reading Maps. Graphing Points on the Coordinate Plane
Lesson Graphing Points on the Coordinate Plane Reading Maps In the middle ages a system was developed to find the location of specific places on the Earth s surface. The system is a grid that covers the
More information2.3 Quick Graphs of Linear Equations
2.3 Quick Graphs of Linear Equations Algebra III Mr. Niedert Algebra III 2.3 Quick Graphs of Linear Equations Mr. Niedert 1 / 11 Forms of a Line Slope-Intercept Form The slope-intercept form of a linear
More informationLesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
More informationDeveloping Algebraic Thinking
Developing Algebraic Thinking DEVELOPING ALGEBRAIC THINKING Algebra is an important branch of mathematics, both historically and presently. algebra has been too often misunderstood and misrepresented as
More informationWhat You ll Learn. Why It s Important
Many artists use geometric concepts in their work. Think about what you have learned in geometry. How do these examples of First Nations art and architecture show geometry ideas? What You ll Learn Identify
More informationGeometry 2001 part 1
Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?
More informationChapter 5. Drawing a cube. 5.1 One and two-point perspective. Math 4520, Spring 2015
Chapter 5 Drawing a cube Math 4520, Spring 2015 5.1 One and two-point perspective In Chapter 5 we saw how to calculate the center of vision and the viewing distance for a square in one or two-point perspective.
More informationGraphing Sine and Cosine
The problem with average monthly temperatures on the preview worksheet is an example of a periodic function. Periodic functions are defined on p.254 Periodic functions repeat themselves each period. The
More information4 The Cartesian Coordinate System- Pictures of Equations
The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the Pythagorean
More informationSolutions to Exercise problems
Brief Overview on Projections of Planes: Solutions to Exercise problems By now, all of us must be aware that a plane is any D figure having an enclosed surface area. In our subject point of view, any closed
More informationh r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.
ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this
More informationconstant EXAMPLE #4:
Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value
More informationC.2 Equations and Graphs of Conic Sections
0 section C C. Equations and Graphs of Conic Sections In this section, we give an overview of the main properties of the curves called conic sections. Geometrically, these curves can be defined as intersections
More informationCHAPTER 3. Parallel & Perpendicular lines
CHAPTER 3 Parallel & Perpendicular lines 3.1- Identify Pairs of Lines and Angles Parallel Lines: two lines are parallel if they do not intersect and are coplaner Skew lines: Two lines are skew if they
More informationAlgebra/Geometry. Slope/Triangle Area Exploration
Slope/Triangle Area Exploration ID: 9863 Time required 60 90 minutes Topics: Linear Functions, Triangle Area, Rational Functions Graph lines in slope-intercept form Find the coordinate of the x- and y-intercepts
More information3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage
Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine
More informationGrade 5 Logical Reasoning
ID : F-5-Logical-Reasoning [1] Grade 5 Logical Reasoning For more such worksheets visit www.edugain.com Answer the questions (1) How many triangles are there in this figure? (2) Kimberly remembers that
More informationA A B B C C D D. NC Math 2: Transformations Investigation
NC Math 2: Transformations Investigation Name # For this investigation, you will work with a partner. You and your partner should take turns practicing the rotations with the stencil. You and your partner
More informationUnit 8 Trigonometry. Math III Mrs. Valentine
Unit 8 Trigonometry Math III Mrs. Valentine 8A.1 Angles and Periodic Data * Identifying Cycles and Periods * A periodic function is a function that repeats a pattern of y- values (outputs) at regular intervals.
More informationUse smooth curves to complete the graph between and beyond the vertical asymptotes.
5.3 Graphs of Rational Functions Guidelines for Graphing Rational Functions 1. Find and plot the x-intercepts. (Set numerator = 0 and solve for x) 2. Find and plot the y-intercepts. (Let x = 0 and solve
More information01. a number of 4 different digits is formed by using the digits 1, 2, 3, 4, 5, 6,7, 8 in all possible
01. a number of 4 different digits is formed by using the digits 1, 2, 3, 4, 5, 6,7, 8 in all possible. Find how many numbers are greater than 3000 thousand place can be filled by any one of the digits
More informationGeometry and Spatial Reasoning
Geometry and Spatial Reasoning Activity: TEKS: Treasure Hunting (5.8) Geometry and spatial reasoning. The student models transformations. The student is expected to: (A) sketch the results of translations,
More informationCivil Engineering Drawing
Civil Engineering Drawing Third Angle Projection In third angle projection, front view is always drawn at the bottom, top view just above the front view, and end view, is drawn on that side of the front
More informationUNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS KEY IDEAS 1. A dilation is a transformation that makes a figure larger or smaller than the original figure based on a ratio given by a scale
More informationParallel and Perpendicular Lines on the Coordinate Plane
Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane 1.5 Learning Goals Key Term In this lesson, you will: Determine whether lines are parallel. Identify and write the
More information33. Riemann Summation over Rectangular Regions
. iemann Summation over ectangular egions A rectangular region in the xy-plane can be defined using compound inequalities, where x and y are each bound by constants such that a x a and b y b. Let z = f(x,
More informationVocabulary slope, parallel, perpendicular, reciprocal, negative reciprocal, horizontal, vertical, rise, run (earlier grades)
Slope Reporting Category Reasoning, Lines, and Transformations Topic Exploring slope, including slopes of parallel and perpendicular lines Primary SOL G.3 The student will use pictorial representations,
More informationINTEGRATION OVER NON-RECTANGULAR REGIONS. Contents 1. A slightly more general form of Fubini s Theorem
INTEGRATION OVER NON-RECTANGULAR REGIONS Contents 1. A slightly more general form of Fubini s Theorem 1 1. A slightly more general form of Fubini s Theorem We now want to learn how to calculate double
More informationSheet 5: Projection of Points
Sheet 5: Projection of Points POSITIONS OF A POINT A point may be located in space in any one of the quadrants. It may also lie on any one of the reference planes or both the reference planes. There are
More informationAim #35.1: How do we graph using a table?
A) Take out last night's homework Worksheet - Aim 34.2 B) Copy down tonight's homework Finish aim 35.1 Aim #35.1: How do we graph using a table? C) Plot the following points... a) (-3, 5) b) (4, -2) c)
More informationReview Journal 6 Assigned Work: Page 146, All questions
MFM2P Linear Relations Checklist 1 Goals for this unit: I can explain the properties of slope and calculate its value as a rate of change. I can determine y-intercepts and slopes of given relations. I
More information