8 th Grade Domain 3: Geometry (28%)

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1 8 th Grade Domain 3: Geometry (28%) 1. XYZ was obtained from ABC by a rotation about the point P. (MGSE8.G.1) Which indicates the correspondence of the vertices? A. B. C. A X, B Y, C Z A Y, B Z, C X A X, B Z, C Y D. A Z, B X, C Y 2. Rectangle ABCD is shown in the coordinate plane below. Rectangle RVTS (not shown) has coordinates R(0, 4), V(-9, 4), T(-9, 9), and S(0, 9). Which of the following is true about rectangles ABCD and RVTS? (MGSE8.G.1) A. ABCD RVTS since the image when ABCD is reflected over the y-axis is RVTS. B. ABCD RVTS since the image when ABCD is reflected over the y-axis is not RVTS. C. ABCD RVTS since the image when ABCD is rotated 90 counterclockwise about the origin is RVTS. D. ABCD RVTS since the image when ABCD is rotated 90 counterclockwise about the origin is not RVTS.

2 3. Vanessa is drawing some designs for her invitations. She divides a grid into 4 quadrants and starts by drawing a shape in one of the quadrants. Which shape below shows the image of her design after a reflection in the x-axis? (MGSE8.G.1) A. B. C. D. 4. Which of the following transformation is not a rigid motion? (MGSE8.G.1) A. Dilation B. Reflection C. Rotation D. Translation 5. In the figure below, polygon RSTUV is the image of ABCDE after a series of transformations. If the two polygons are congruent, which side must have the same length as side BC? (MGSE8.G.2) A. CD B. DE C. ST D. TU

3 6. If figure 1 is rotated 90⁰ about the origin, line segment CD would be congruent to which segment in figure 2? (MGSE8.G.1, MGSE8.G.2) A. ZW B A D C B. XW C. BC D. AD 7. Trapezoid ABCD is shown on the coordinate grid below. ABCD is translated to form A B C D (not shown), which is congruent to ABCD. If the coordinates of D are (-1, 3), what is the rule for the translation that maps ABCD onto A B C D? (MCC.8.G.2) A. (x, y) (x 5, y + 6) B. (x, y) (x 6, y + 5) C. (x, y) (x + 6, y 5) D. (x, y) (x + 5, y 6) 8. Which of the following is not a transformations that proves that shape G is congruent to shape H. (MGSE8.G.2) A. Reflect shape G across the x-axis then translate it 6 units right. B. Reflect shape G across the y-axis then reflect it across the x-axis. C. Rotate shape G 180⁰ about the origin D. Rotate shape G 180 about the origin and reflect over the y-axis. 9. ABC is rotated 180 clockwise about the origin to form DEF. What are the coordinate of the vertices of DEF? (MGSE8.G.3) A. A (7, 4), B (4, 2), C (3, 8) B. A (-4, 7), B (-2, 4), C (-8, 2) C. A (4, -7), B (2, -4), C (2, -8) D. (-7, 4), B (-4, 2), C (-3, 8) X W Y Z

4 10. Quadrilateral EFGH, shown in the coordinate plane below, is dilated with the center at the origin to form quadrilateral ABCD. What is the scale factor of the dilation? (MGSE8.G.3) A. 1 4 B. 1 3 C. 3 D What are the coordinates of the image of point P( 3, 7) after a reflection about the line y = 2? (MGSE8.G.3) A. ( 3, 9) B. ( 3, 11) C. (5, 7) D. (7, 7) 12. If Figure ABCD is translated so that the image of A is A' at ( 3,2), then the coordinates of the image of point B will be (MGSE8.G.3) A. (0,0) B. (-1,4) C. (-2,-1) D. (-3,1) 13. An equilateral triangle with side lengths of 6 undergoes dilation with a scale factor of 3:7. What are the side lengths of the image? (MGSE8.G.4) A. X = 10 B. X = 12 C. X = 14 D. X = 16

5 14. Using transformations explain how you know that figure A and figure B are similar. (MGSE8.G.4) A. Rotate figure A 90⁰ about the origin and all sides and vertices correspond. A B. Rotate figure A 180⁰ about the origin and all sides and vertices correspond. C. Rotate figure A 270⁰ about the origin and all sides and vertices correspond. B D. Rotate figure A 0⁰ about the origin and all sides and vertices correspond. 15. ABC and DEF are shown on this coordinate grid. Describe a sequence of transformations that verify that these triangles are geometrically similar. (MGSE8.G.4) 16. Triangle BAD with vertices B(1, 1), A(3, 0), D(3, 3) is translated 3 units to the left then reflected over the x-axis. What are the coordinates of the image of the original triangle after the transformations are performed? Use the grid below to perform the transformations. (MGSE8.G.4) A. B (-2, -1), A (0, 0), D (0, -3) B. B (-2, 1), A (0, 0), D (0, 3) C. B (1,, -2), A (0, 0), D (3, 0) D. B (-1, -2), A (0, -3), D (0, 0)

6 17. Lines l and m are parallel to one another and cut by transversals s and t. (MGSE8.G.5) What is the measure of angle x? A. 40 B. 80 C. 120 D Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20 and angle BCA measures 30. What are the measures of angles x and y? Explain. (MGSE8.G.5) 19. Find the values of y and z. (MGSE8.G.5) A. y = 35, z = 55 B. y = 37, z = 49 C. y = 49, z = 37 D. y = 55, z = If a and b are parallel lines that are cut by transversal c, and m 8 = 57, what is the measure of 3? (MGSE8.G.5) A. 57 B. 90 C. 123 D. 180

7 MGSE8.G Two sailboats leave Key Largo, Florida. One of the sailboats travels 3 miles east and then 4 miles north. The second sailboat travels 8 miles south and 6 miles west. How far apart in miles, are the boats. A. 14 miles B. 15 miles C. 17 miles D. 19 miles MGSE8.G A can of drink is in the shape of a cylinder with height 15 cm and radius 4 cm. What is the length of the longest straw that will fit inside the can? A. 17 cm B. 19 cm C. 21 cm D. 23 cm MGSE8.G The distance between the bases on a baseball diamond is 90 feet as shown to the right: What is the distance (d), in feet, between home plate and second base? Round your answer to the nearest whole number. (Use for 2) A. 90 B. 127 C. 135 D. 180 MGSE8.G.7

8 24. The cube below has a length of 12 in. What would be the length of a diagonal along either of its faces? A inches B inches C inches D inches MGSE8.G What is the approximate volume of the cone to the right? (Use 3.14 for π) A. 70 cm 3 B. 183 cm 3 C. 549 cm 3 D. 733 cm 3 MGSE8.G The right cylinder has a radius of 3 inches and a height of 4 inches. What is the approximate volume, in cubic inches, of the cylinder? A. 12π in 3 B. 36π in 3 C. 48π in 3 D. 60π in 3

9 MGSE8.G The right cylinder and right cone shown to the right have the same radius and volume. The cylinder has a height of 12 inches. What is h, the height of the cone? A. 18 inches B. 24 inches C. 36 inches D. 42 inches MGSE8.G Tawana has a spherical bottle shaped like a basketball. Each cubic inch of the bottle can hold 2 cups of water. If the bottle is completely full, approximately how many cups of water can it hold? (Use 3.14 for π) A. 452 cups B. 904 cups C cups D cups MGSE8.G What is the approximate distance in inches between the two endpoints of the segment on the right? A. 1.4 inches B. 2.8 inches C. 7.1 inches D. 8.2 inches

10 MGSE8.G Use your knowledge of the Pythagorean Theorem to find the approximate distance between P 1 and P 2. Round your answer to the nearest whole number. A. 7 B. 9 C. 12 D. 17 MGSE8.G Graph the points: (5, 5) and (-6, -4) on a coordinate plane and calculate the distance between them. Round your answer to the nearest hundredth. A B C D MGSE8.G The segment to the right represents the string that a fisherman used to measure the length of an eel that got caught in his net. What was the approximate length (in feet) of the eel? Round your answer to the nearest tenth? A. 7.6 feet B. 8.7 feet C. 9.4 feet D feet

11 MGSE8.G Do 12, 5 and 13 represent the possible side lengths of a right triangle? Explain. A. Yes, because > 13 B. Yes, because = 13 2 C. No, because D. No, because > 5 MGSE8.G What kind of triangle is it when a 2 + b 2 < c 2? A. Right triangle B. Obtuse triangle C. Acute triangle D. None of the above MGSE8.G The square to the right has a diagonal of 15 2 inches, what is the perimeter of the square? A. 30 inches B. 45 inches C. 60 inches D. 225 inches MGSE8.G , 9, 10 represent the side lengths of a triangle. Is the triangle represented by the given side lengths a right triangle? Explain. A. Yes, because = 10 2 B. Yes, because > 10 C. No, because D. No, because

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