6. Find P, the image of P( 3, 6), after a reflection across the line y = x.

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1 Name: 1. What is the image of point after a rotation of 90 in the counterclockwise direction? 4. is the image of. Which of the following rotations could be used to perform this transformation? I. 90 counterclockwise G E II. 90 clockwise III. 270 clockwise IV. 270 counterclockwise F H... E. F 2. What is the image of ( 4, 1) after a rotation of 180 clockwise?. ( 1, 4). (1, 4). (4, 1). (1, 4). II only. III only. II and IV. I and III 3. Select the letters that would appear the same after a 180 rotation about the center. I. II. H III. R 5. If a point in Quadrant III is reflected in the x-axis, its image will lie in Quadrant.. I. II. IV. on the y-axis IV. S. I only. II only. III only. II and IV 6. Find P, the image of P( 3, 6), after a reflection across the line y = x.. (6, 3). (3, 6). (3, 6). (6, 3) page 1

2 7. What is the image of point after a rotation of 90 in the counterclockwise direction followed by a reflection in the x-axis? 11. Triangle is an image of the other triangle. What kind of transformation is shown? G E F H... E. H 8. What are the coordinates of (1, 2) after a translation down 2 units and then a rotation of 180 in a counterclockwise direction about (0, 0)?. (0, 1). (1, 1). ( 1, 0). (1, 0). translation. reflection. dilation. rotation 12. What is the mapping for the reflection where maps to? 9. If the triangle XYZ is reflected about the vertical line x = 3, what are the new coordinates for Z?. (2, 2). (2, 2). (8, 2). (8, 2). (x, y) ( y, x). (x, y) ( x, y). (x, y) (x, y). (x, y) ( y, x) 10. Two shapes coincide if one shape can be laid on top of the other and there is an exact match between their points. onsider these four shapes: I. equilateral triangle II. square III. rectangle 13. Which set of numbers can not represent the lengths of the sides of a triangle?. {6, 8, 11}. {7, 5, 6}. {7, 18, 11}. {9, 12, 19} IV. parallelogram Which of the shapes will coincide with itself if rotated by 90?. I only. II only. II and III only. all except II page 2

3 14. What is the measure of the largest angle in the accompanying triangle? 20. Find a Find b If the perimeter of an equilateral triangle is represented by 6x 9, the length of a side of this triangle can be expressed as. x 9. 2x 3. 3x 3. x 16. State the congruence relation for FLE and FUE... SS. SSS 22. Find the exact value of y.. not necessarily congruent State the congruence relation for WO and IRO. Use only the markings in the diagram.. S. SS 23. Find the area of the triangle SS. not necessarily congruent 18. Find the length of side x. 24. Which of the following ratios is the tangent of an angle? hypotenuse adjacent hypotenuse opposite.. adjacent hypotenuse opposite adjacent 19. In the diagram, = 9, = 5, and = 12. If m = 90, what is the perimeter of triangle? 25. Given the triangle shown, which of the following is true?. sin = c b. cos = c b tan = b a. sin = b c page 3

4 26. Which of the following statements is incorrect for XYZ?. sin Z = YZ = In the triangle shown, determine to the nearest degree tan Y = cos X = What is the measure of to the nearest degree? 27. Given the following triangle, cos θ = What is the length of side to one decimal place? ladder is leaning against a tree. If the angle that the ladder makes with the ground is 60, and the ladder is 10 feet long, how far is the base of the ladder from the tree?. 5 ft. 15 ft. 20 ft. 25 ft In triangle RST, RS = 9 and m R = 40, find the length of ST to the nearest tenth The angle of elevation to the top of a flagpole is 52. If the angle of elevation was measured 23 m from the center of the flagpole s base, what is its height to 1 decimal place? m m m m In NPQ, calculate N to the nearest degree meter long wire is attached to the top of a telephone pole 7 meters tall. What is the exact measure of the angle the wire makes with the ground? page 4

5 36. Join the points on the coordinate plane. What is the area of parallelogram? 39. Which of the following graphs represents the relation x 2 + y 2 = 16? cm cm cm cm What is a reasonable estimate for circumference of one of the circles? 40. What is the equation of the circle shown below?. (x + 2) 2 + (y 2) 2 = 9. (x 2) 2 + (y + 2) 2 = 3. (x + 2) 2 + (y 2) 2 = 3. less than 16 cm. less than 12 cm. (x + 2) 2 + (y 2) 2 = 1. less than 26 cm. less than 32 cm 38. ased on the diagram below, what is a reasonable estimate for the area of the shaded region? 41. Write the equation of the circle with center ( 2, 3) and radius 2.. (x 2) 2 + (y + 3) 2 = 4. (x + 2) 2 + (y 3) 2 = 4. (x 2) 2 + (y + 3) 2 = 2. (x + 2) 2 + (y 3) 2 = etermine the center of the circle if the endpoints of a diameter are ( 2, 4) and (6, 8).. less than 15 units 2. less than 20 units 2. less than 25 units 2. less than 50 units 2. (2, 12). (2, 2). (4, 4). (8, 12) 43. One end of a line segment has the coordinates ( 3, 8). If the middle point is (5, 8), then what are the coordinates of the other endpoint?. (13, 24). (10, 16). (7, 8). (15, 64) 44. The coordinates of the endpoints of the diameter of a circle are ( 1, 3) and (3, 6). Find the radius of the circle page 5

6 45. In the accompanying diagram, two concentric circles have radii of 9 and 5, respectively. In terms of π, the area of the shaded region is. 56π. 16π. 8π. 4π 50. Lenny made a cube in technology class. Each edge measured 1.5 cm. What is the volume of the cube in cubic centimeters? Mrs. yer is painting the outside of her son s toy box, including the top and bottom. The toy box measures 3 feet long, 1.5 feet wide, and 2 feet high. What is the total surface area she will paint?. 9.0 ft ft ft ft In the accompanying diagram, a circle with radius 4 is inscribed in a square. 52. Luis is going to paint a basketball court on his driveway, as shown in the diagram below. This basketball court consists of a rectangle and a semicircle. What is the area of the shaded region? π π. 64p 8π. 16 8π 47. The length of a rectangle is 12 more than the width. The area is 325. Which equation best represents the situation if W represents the width of the rectangle?. w w + 12 = 0. w 2 12w 325 = 0. w w 325 = 0. w 2 325w + 12 = 0 Which expression represents the area of this basketball court, in square feet? π π π 53. right circular cylinder has a base whose area is 12π. If the height of the cylinder is 6, the volume of the cylinder is 48. The base of a triangle is 4 units more than the height. The area of the triangle is 48 square units. If the height is represented by x, which equation could be used to find the measure of the height of the triangle?. x(x + 4) = x(x + 4) = (2x + 4) = x(x 4) = The perimeter of a square is 4a. What is the area of the square?. a 2. 4a π. 24π. 36π. 72π 54. box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box? in. 16 in. 8 in. 4 in 55. The volume of a cylindrical can is 32π cubic inches. If the height of the can is 2 inches, what is its radius, in inches? page 6

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