GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)

Transcription

1 GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance Formula and the Pthagorean Theorem to find the distance between two points. 1. Graph AB when A(-2, 3) and B (1, 0). 2. Find the length of CD. C D 3. Find the coordinate of the midpoint of CD from problem Simplif. 5. Use Pthagorean Theorem to solve for AB.

2 Find the coordinates of the midpoint of EF with endpoints E(-2, 3) and F(5, -3). Find the coordinates of the midpoint of MN with endpoints M(-1,-5) and N(-6,-3). The Distance Formula is used to calculate the distance between two points in a coordinate plane. Find the distance between K(-2, -3) and E(3, -5). Use the distance formula to find FG and JK. Then determine whether FG JK. Step 1: Find the coordinates of each point. F J G K Step 2: Use the Distance Formula to find the length of JK and FG. Step 3: Determine if segments are congruent.

3 PYTHAGOREAN THEOREM Instead of distance formula, ou can often use the Pthagorean Theorem! In a right triangle, the two sides that form the right angle are the. The side across from the right angle that stretches from one leg to the other is the. In the diagram, a and b are the legs of the right triangle. The longest side is called the hpotenuse ad has length c. b a c Use the Pthagorean Theorem to find the distance of each segment in the graph. Use the Pthagorean Theorem to find the missing part of each right triangle below. a = 5, b = 7, c =? a = 12, b =?, c = 27 a =?, b = 6, c = 12

4 Finding the Distances in the Coordinate Plane Use the Distance Formula and the Pthagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(-2, -5). HOMEWORK 1.6: #1-4, 6-10, 14, 16, 17, 21, 23, 36.

5 Section 3.5 Slopes of Lines (2) Objectives: Find the slope of a line. Use slopes to identif parallel and perpendicular lines. WARM UP Find the value of the variable. (Remember to use order of operations.) 1. b = (7 5) ( 8 3) 2. n = (( 3) 6) ( 5 ( 1)) 3. = 4 ( 4) d = So what s the deal with dividing b zero? What is 10 2? What is 0 2? What is 10 0? No such number eists, therefore, an number divided b zero is said to be undefined. SLOPE: The slope of a line in a coordinate plane is a number that describes the steepness of the line. An two points on a line can be used to determine the slope.

6 Finding the Slope of a Line Use the slope formula to determine the slope of each line. AC DC AB AD The ratios and are called opposite reciprocals. If a line has a slope of, then the slope of a perpendicular line is. List the slope of a line perpendicular to a line with slope: a. 3 2 b. 1 4 c. 5 6 d. 0

7 Are the lines with slopes 2 12 and perpendicular? 3 8 Determining Whether Lines Are Parallel, Perpendicular, or Neither Graph each pair of lines. Use their slopes to determine whether the are parallel, perpendicular, or neither. UV and XY for U(0, 2), V( 1, 1), X(3, 1), and Y( 3, 3) Determining Whether Lines Are Parallel, Perpendicular, or Neither. Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. WX and YZ for W(3, 1), X(3, 2), Y( 2, 3), and Z(4, 3) Determining Whether Lines Are Parallel, Perpendicular, or Neither. Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. BC and DE for B(1, 1), C(3, 5), D( 2, 6), and E(3, 4) HOMEWORK 3.5: 1-5, 7-13, 15, 16, 17

8 Section 3.6 Lines in the Coordinate Plane (3) Objectives: Graph lines and write their equations in slope-intercept and point-slope form. Classif lines as parallel, intersecting, or coinciding. The equation of a line can be written in man different forms. The point-slope and slope-intercept forms of a line are equivalent. Because the slope of a vertical line is undefined, these forms cannot be used to write the equation of a vertical line. Write the equation of each line in the given form: the line with slope 6 through (3, 4) in point-slope form Write the equation of each line in the given form: the line through ( 1, 0) and (1, 2) in slope-intercept form Graph the line: Graph the line: 3 = 2( + 4)

9 Graph the line = -4. Graph the line = -2. Identif the slope Identif the slope Lines that coincide are the same line, but the equations ma be written in different forms. (Coincide: same slope and same b ) The lines can be,,, or none of the above. A sstem of two linear equations in two variables represents two lines. Perpendicular Opposite reciprocal slopes Determine whether the lines are parallel, intersect/perpendicular, coincide or none of them. a. = and = -3 4 b. c. 3 = - ½ and 5 = 2( + 3) d. 2 = 4 8 and 4 2 = 8 HOMEWORK 3.6: 1-11, 12-22, 24-31

10 Section 10.1 & 10.2: Developing Formulas Triangle, Quadrilaterals, Circles and Regular Polgons (4) Objectives: Develop and appl the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special quadrilaterals. Develop and appl the formulas for the area and circumference of a circle. Develop and appl the formula for the area of a regular polgon. The height of a parallelogram is measured along a segment perpendicular to a line containing the base. Finding Measurements of Parallelograms Find the area of the parallelogram. 10 ft 22 ft Finding Measurements of Parallelograms Find the base of the parallelogram in which h = 56 d and A = 168 ards 2 Finding Measurements of Parallelograms Find the area of the parallelogram. Step 1: Use the Pthagorean Theorem to find the height h. Step 2: Use h to find the area of the parallelogram.

11 Finding Measurements of Triangles and Trapezoids. Find the area of the trapezoid. 7 ft 11 ft 11 ft 17 ft Finding Measurements of Triangles and Trapezoids. Find b2 of the trapezoid, in which A = 231 mm 2 Find the area of the triangle. Find the area of the triangle. The diagonals of a rhombus or kite are perpendicular, and the diagonals of a rhombus bisect each other. Finding Measurements of Rhombuses and Kites Find the area of the kite with diagonals 12 cm and 18 cm. Finding Measurements of Rhombuses and Kites Find d2 of a kite in which d1 = 14 in and A = 238 in 2.

12 Finding Measurements of Rhombuses and Kites. Find the area of the kite 10.2 A is the locus of points in a plane that are a fied distance from a point called the. A circle is named b the smbol and its center. A has radius r = AB and diameter d = CD. The irrational number is defined as the ratio of the circumference C to the diameter d, or. Solving for C gives the formula C = d. Also d = 2r, so C = 2r. Finding Measurements of Circles Find the area and the circumference of K in terms of. HELPFUL HINT: The ke gives the best possible approimation for on our calculator. Alwas wait until the last step to hit that button and round. Cooking Application A pizza-making kit contains three circular baking stones with diameters 24 cm, 36 cm, and 48 cm. Find the area of each stone. Round to the nearest tenth.

13 POLYGONS: 4 sided polgon: 5 sided polgon: 6 sided polgon: 7 sided polgon: 8 sided polgon: 9 sided polgon: 10 sided polgon: 12, 15, 18, etc. The is equidistant from the vertices. The is the distance from the center to a side. A has its verte at the center, and its sides pass through consecutive vertices. Each central angle measure of a regular n-gon is. Regular pentagon DEFGH has a center C, apothem BC, and central angle DCE. Finding the Area of a Regular Polgon Find the area of the regular octagon with side length 10 ft and an apothem of 8 ft. to the nearest tenth. Finding the Area of a Regular Polgon Find the area of a regular pentagon with apothem of 4 m.

14 Quadrilateral Kite Parallelogram Trapezoid Rectangle Rhombus Square 10.1 HOMEWORK: #1-8, 11, 12, 15, 17, 19, HOMEWORK: #2-6, 10, 14.

15 Section 10.4 Perimeter and Area in the Coordinate Plane (5) Objectives: Find the perimeters and areas of figures in a coordinate plane. WARM-UP: Write the distance formula: Write the slope formula: Pthagorean Theorem What is the difference between the area of a figure and the perimeter of a figure? LET S REVIEW SIMPLIFYING RADICALS: Graph the figure with vertices (4,0), (1, 0), (1, 4) and (4, 4), Find the area and the perimeter of the polgon.

16 Find the perimeter of the polgon with vertices E( 4, 1), F( 2, 3), G( 2, 4). Find the perimeter of the polgon with vertices K( 2, 4), L(6, 2), M(4, 4), and N( 6, 2). Draw and classif the polgon with vertices E( 1, 1), F(2, 2), G( 1, 4), and H( 4, 3). Find the perimeter of the polgon. Step 1 EFGH appears to be a parallelogram. How will ou prove the shape is a parallelogram? (Remember we have several was to prove a quadrilateral is a parallelogram.) STEP 2: What is the perimeter of EFGH. Homework 10.4: #3-8 (find perimeter ONLY), (find perimeter ONLY).