Slide 1 / 52 The oordinate Plane Slide 2 / 52 Table of ontents ntroduction Vocabulary raphing ordered pairs unction amilies Slide 3 / 52 ntroduction Slide 4 / 52 The development of the oordinate or artesian plane is often credited to the rench philosopher and mathematician, Rene escartes. t is said that escartes first came up with the idea for the plane as he lay in bed watching several flies crawl across his tiled ceiling; as he observed their movement he realized that he could use the intersecting lines formed by the tiles to describe a fly s location. lthough historical evidence suggests that a " contemporary of escartes, Pierre de ermat, did more to develop the coordinate system, Rene escartes work certainly revolutionized mathematics by describing the properties of the plane and using it as the first systematic link between uclidean geometry and algebra. " ogito,ergo sum Pierre, bring me my fly swatter! (1,1) x Rene escartes 1596-165 (-1,-1) (2,-2) y Slide 5 / 52 Return to Table of ontents The well known quote; "ogito,ergo un act sum" ( think,therefore am) is attributed to Rene escartes. Slide 6 / 52 Return to table of contents VOULRY The coordinate plane is divided into four sections called quadrants. ach quadrant is numbered using the Roman numerals through V, in a counter-clock wise direction. Return to Table of ontents
Slide 7 / 52 Slide 8 / 52 c Slide the "" onto the coordinate plane y - axis x - axis The oordinate plane is also called the artesian plane. One way to remember how the quadrants are numbered is to write a big "" on top of the plane. The "" will begin in quadrant and end in quadrant V. The quadrants are formed by two intersecting number lines called axes. The horizontal line is the x-axis. The vertical line is the y-axis. Slide 9 / 52 Slide 1 / 52 Origin (, ) The point at which the x and y axes intersect is called the origin. The coordinates of the origin are (, ). Slide 11 / 52 Points can be plotted on the plane using one coordinate from each of the axes. These sets are called ordered pairs. The x coordinate always appears first in these pairs. The y coordinate appears second. (x, y) Slide 12 / 52 ach of the quadrants can be identified by the properties of the numbers that fall within their plane. Remember the ordered pairs are always of the form (x, y) 1 What points are in quadrant? (-,+) ( +,+) (-,-) (+,-)
Slide 13 / 52 2 What points are in quadrant? Slide 14 / 52 3 What points are in quadrant V? Slide 15 / 52 Slide 16 / 52 4 What points are in quadrant? 5 What point is closest to the origin? is Slide 17 / 52 Slide 18 / 52 Return to table of contents raphing Ordered Pairs To graph an ordered pair, such as (3,2): start at the origin (,) move left or right on the x-axis depending on the first number then move up or down from there depending on the second number plot the point (3,2) Return to Table of ontents
Slide 19 / 52 Slide 2 / 52 To graph (-3, 4): Start at the origin and then move 3 left, up 4 To graph (-3, -2): Start at the origin and then move 3 left, down 2 (-3, 4) (-3, -2) Slide 21 / 52 Slide 22 / 52 To graph (5, -3): Start at the origin and then move 5 right, down 3 Place the star on (2,8) in quadrant Place the triangle on (-4, 4) in quadrant Place the square on (-7, -3) in quadrant Place the circle on (1, -4) in quadrant V (5, -3) Slide 23 / 52 Place the circle on (-7,-5) Place the star on (4,9) Place the triangle on (-6,2) Place the square on (3,-9) n which quadrant is the circle? Slide 24 / 52 Match the coordinate points below with points - on the coordinate plane. Move each rainbow circle to check your answers. (-9,-4) (2,-2) (9,) (,6) (5,7) (-3,2)
Slide 25 / 52 6 The point (-5, 4) is located in quadrant. Slide 26 / 52 7 The point (7, -2) is located in quadrant. V V Slide 27 / 52 8 The point (4, 5) is located in quadrant. Slide 28 / 52 9 The quadrant where the x & y coordinates are both negative is quadrant. V V Slide 29 / 52 Slide 3 / 52 1 When plotting points in the artesian Plane, you always start at. List the coordinates of each point the x - axis the origin the y-axis the oordinate Plane (,)
Slide 31 / 52 Slide 32 / 52 List the coordinates of each point List the coordinates of each point Slide 33 / 52 Slide 34 / 52 Open ended Questions Remember to: *Read the question carefully and think about the answer. *nswer all parts of the question. *Show your work and explain your answer. You can answer the questions using words, tables, diagrams or pictures. Slide 35 / 52 Vocabulary Review oordinate Plane: the two dimensional plane or flat surface that is created when the x-axis intersects with the y-axis. lso known as a coordinate graph and the artesian plane. 11 Slide 36 / 52 f the x-coordinate is positive, the point to be plotted will be in quadrant. Quadrant: any of the four regions created when the x-axis intersects the y-axis. They are usually numbered with Roman numerals. & V x-axis: horizontal number line that extends indefinitely in both directions from zero. (Right- positive Left- negative) & V y-axis: vertical number line that extends indefinitely in both directions from zero. (Up- positive own- negative) Origin: the point where zero on the x-axis intersects zero on the y-axis. The coordinates of the origin are (,).
Slide 37 / 52 Slide 38 / 52 12 f the y-coordinate is positive, the point to be plotted will be in quadrant. 13 f the x - coordinate is negative and the y-coordinate is positive, the point to be plotted will be in quadrant. & & & V & V Slide 39 / 52 Slide 4 / 52 14 f the x - coordinate is positive and the y-coordinate is negative, the point to be plotted will be in quadrant. 15 Point is located at (-3, 2) True alse V Slide 41 / 52 Slide 42 / 52 16 Point is located at (-5, 1) 17 Point is located at (-2, 3) True alse True alse
18 True Point is located at (-2, ) Slide 43 / 52 Slide 44 / 52 unction amilie s alse family of functions is a group of functions with shared traits. The parent function is the most basic function in a family. Linear unctions Slide 45 / 52 The parent function for all linear functions is y = x omplete the table, plot the points and then connect them. -3-2 -1 1 2 3 X y = x Y Put arrows at the end of the line to indicate the line goes on forever. -4-3 -2-1 1 2 3 4 X Y Slide 46 / 52 bsolute Value unctions ill in the table for y = l x l Then plot the points and connect them. Return to Table of ontents PULL PULL Slide 47 / 52 Slide 48 / 52 Quadratic unctions omplete the table for y = x 2 Then plot the points and connect them -3-2 -1 1 2 3 X Y Match the correct equation with the graphed function y = x y = x 2 y = l x l PULL PULL
19 The function graphed is y = x Yes No Slide 49 / 52 Slide 5 / 52 2 The function graphed is y = x 2 Yes No Slide 51 / 52 Slide 52 / 52 21 The function graphed is y = l x l Yes No