GRADE 8 ADAPTED NJDOE ASSESSMENT. Assessed Standards: 8.G.1 8.G.2 8.G.3 8.G.4 8.G.5. (To be administered after NPS Grade 8 Scope and Sequence Unit 2)
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1 ADAPTED NJDOE ASSESSMENT GRADE 8 (To be administered after NPS Grade 8 Scope and Sequence Unit 2) Assessed Standards: 8.G.1 8.G.2 8.G.3 8.G.4 8.G.5 The Newark Public Schools - Office of Mathematics 2013
2 Name Period Date Grade 8 Unit 2 For multiple choice questions, circle the best answer. For all other questions, respond in the space provided. 1. Angle ABC in the coordinate plane below will be rotated 90 degrees counterclockwise about the origin. What are the coordinates of the image of point A? a. 0, 3 b. 0, 3 c. 3, 3 d. 3, 0
3 2. Parallel lines and n (not shown) were each translated. Could lines t and u shown in the coordinate plane below be the image of lines and n after translation? Explain your reasoning.
4 3. Part A What are the coordinates of the image of point B when line segment AB in the coordinate plane above is reflected about the x-axis? Part B What are the coordinates of the image of point B when line segment AB in the coordinate plane above is reflected about the y-axis? Part C What are the coordinates of the image of point B when line segment AB in the coordinate plane above is reflected about the origin?
5 4. Describe a sequence of transformations that can be used to show that triangle ABC is congruent to triangle XYZ.
6 5. Triangle ABC is shown in the coordinate plane below. Triangle XYZ (not shown) is located in the coordinate plane with vertices at points X 9, 0, Y 7, 4, and Z 7, 0. Part A Which of the following transformations shows that triangle ABC is congruent to triangle XYZ? a. Triangle ABC is translated 7 units to the right and 2 units down. b. Triangle ABC is translated 14 units to the right and 2 units down. c. Triangle ABC is reflected over the x-axis and translated 2 units down. d. Triangle ABC is reflected over the y-axis and translated 2 units down. Part B Explain your reasoning for the answer you gave in part A.
7 6. 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? 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.
8 7. A transformation maps a preimage triangle to the image triangle shown in the coordinate plane below. If the preimage triangle is reflected over the y-axis to get the image triangle, what are the coordinates of the vertices of the preimage triangle? a. 4, 1, 6, 1, 6, 6 b. 4, 1, 6, 1, 6, 6 c. 4, 6, 4, 1, 6, 1 d. 4, 1, 6, 1, 6, 6
9 8. The circle shown in the coordinate plane below is the preimage under a dilation centered at the origin with scale factor 2. Which of the following points is NOT on the image of the dilation? a. 6, 6 b. 0, 0 c. 0, 6 d. 6, 6
10 9. Parallelogram EFGH is shown in the coordinate plane below. Rotate EFGH 90 degrees clockwise about the origin and then translate it 3 units down. Label the resultant image PQRS.
11 10. Quadrilateral ABCD, shown in the coordinate plane below, is dilated with the center at the origin to form quadrilateral EFGH. What is the scale factor of the dilation? a. b c. 3 d. 4
12 11. Triangle XYZ is shown in the coordinate plane below. Dilate XYZ with center 0, 0 and scale factor 3. 2 Label the resultant image PQR.
13 12. Quadrilaterals JKLM and WXYZ are shown in the coordinate plane below. Quadrilateral WXYZ is the image of quadrilateral JKLM under a transformation. Which of the following best describes the transformation? a. A dilation with center 0, 0 with a scale factor of 2. 3 b. A dilation with center 0, 0 with a scale factor of 3. 2 c. A translation 2 units to the left and 3 units down. d. A translation 2 units to the right and 3 units up.
14 13. Triangles ABC and XYZ are shown in the coordinate plane below. Are triangles ABC and XYZ similar? Justify your answer using one or more transformations.
15 14. Triangles ABC, DEF, JKL, and PQR can be placed in the coordinate plane below and are related to each other in the following manner. Triangle ABC is reflected over the x-axis to get triangle DEF. Triangle DEF is translated 6 units to the right and 4 units down to get triangle JKL. A transformation is applied to triangle JKL to get triangle PQR. Triangle PQR is similar to triangle ABC but NOT congruent to triangle ABC. Which of the following could describe the transformation applied to triangle JKL to get triangle PQR? a. Triangle JKL is rotated 90 counterclockwise about the origin to get PQR. b. Triangle JKL is rotated 180 about the origin to get PQR. c. Triangle JKL is dilated with a scale factor of 1 with the center at the origin to get PQR. d. Triangle JKL is dilated with a scale factor of 5 with the center at 3, 4 to get PQR.
16 15. Two quadrilaterals are shown in the coordinate plane below. Quadrilateral ABCD was dilated with a scale factor of 2 with the center at the origin and then rotated 180 about the origin to get the quadrilateral in Quadrant IV. Part A Label the image quadrilateral in Quadrant IV using W, X, Y, and Z. Part B Write a sentence that describes the relationship between the two quadrilaterals using the word congruent or the word similar.
17 16. In the figure below, lines AB and CD are parallel, line EF is a transversal, and the measure of angle DGF is 60. Part A Give the measure of angle BHF, and justify your answer using one or more transformations. Part B Give the measure of angle AHE, and justify your answer. Part C Give the measure of angle BHE, and justify your answer.
18 17. Based on the figure below, determine whether each given statement must be true, and briefly explain why. Statement Must the statement be true? (Yes or No) Explain why. Line is parallel to line m. Line t is parallel to line u. x 110 y 70
19 18. In the figure below, lines AB and CD are parallel and line EF is a transversal. Give an informal argument showing that angles CGH and BHG are congruent.
20 19. In the figure below, 23. x = Is line k parallel to line m? Explain your answer.
21 20. In the figure below, line AB is parallel to line ED. Two angles in triangle ACB are shown to have measures equal to two other angles in the figure. Use the figure to explain why the sum of the measures of the angles of triangle ACB is equal to 180 degrees. 21. Are the two triangles shown below similar triangles? Explain your answer.
22 22. In the figure below, does a = 120? Explain your answer.
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