Unit One Test (Transparallellines) B. The reflection of line 1 over the x -axis and the translation of line 2 four units to the left.
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1 Name: Date: 1. The coordinate grid shows the intersection of line 1 and line 2. Which transformations on lines 1 and 2 will result in a pair of lines intersecting at the same angle measurements as those formed by the intersection of line 1 and line 2? A. The reflection of line 1 over the x -axis and the translation of line 2 four units up. B. The reflection of line 1 over the x -axis and the translation of line 2 four units to the left. C. The reflection of line 1 over the x -axis and the reflection of line 2 over the line D. The reflection of line 1 over the x -axis and the reflection of line 2 over the line 1
2 2. Lines m and n are graphed on the coordinate grid shown. Part A Lines m and n are translated 4 units down and 8 units left. Sketch a graph to represent the new location of lines m and n. Label the new location of line m as line e and the new location of line n as line f. Part B Lines m and n are reflected across the x -axis. Explain the effect this reflection has on the lines. Has the distance between the lines changed? Part C Are the lines m and n parallel, perpendicular, or intersecting lines? Describe what happens to the lines after a clockwise rotation of 90 is applied to the lines. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 2
3 3. Right triangle JKL is graphed on a coordinate grid. Unit One Test (Transparallellines) Part A If the triangle is reflected across the y -axis, what would be the vertices of the reflected triangle? Label the new vertices as and Part B What are the lengths of line segments JK and KL? Part C What is the length of line segment Show your work. Part D What is the relationship of triangles JKL and Explain your answer. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 3
4 4. Which transformation can result in a new figure that is not congruent to the original figure? A. dilation B. reflection C. rotation D. translation 4
5 5. Mr. Novak draws a figure on a coordinate grid. He begins to construct a new figure congruent to the figure shown by points and as shown in the coordinate grid. Part A Mr. Novak used two different transformations to create the new figure. Based on the location of points what would be the coordinates of and and Part B Describe a sequence of transformations which would result in the new figure being congruent to the original figure based on point and Part C Create a similar figure, but not congruent, to Mr. Novak s new figure in quadrant I. What are the coordinates of and Part D Describe the sequence of transformations you used to create the figure in Part C. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 5
6 6. Fill in the blank. All are either similar or congruent to each other. A. circles B. triangles C. rectangles D. parallelograms 7. A city park has two congruent flowerbeds. The flowerbeds are shown as triangles PQR and STU. Which angle is congruent to P? A. R B. S C. T D. U 8. The triangles shown are congruent. Which of the following two sides MUST be proportional? A. CM and SV B. CM and MT C. CT and VU D. CT and MT 6
7 9. A marine scientist is looking for a specific organism in the ocean. The triangle shows the part of the ocean the scientist previously studied. The scientist needs to modify his location. The triangle will be reflected over the line a vertex of the reflected triangle? Which coordinate is A. B. C. D. 7
8 10. A graphic artist is creating a design with two rectangles. The grid shows the first rectangle. The artist wants to rotate the first rectangle rectangle? about the origin. Which coordinate is a vertex of the second A. B. C. D. 8
9 11. The diagram below shows the location of on a coordinate plane. Suppose that is rotated 180 clockwise about the origin. What are the coordinates of the image of point E? A. ( 2, 4) B. ( 4, 2) C. (4, 2) D. ( 4, 2) This online assessment item contains material that has been released to the public by the Massachusetts Department of Education. 9
10 12. Look at the triangles below. Which of these triangles are most likely similar? A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 3 and 4 10
11 13. Rectangle P and rectangle Q are graphed on a coordinate grid. Part A Describe a sequence of at least two transformations that would prove or disprove whether or not rectangle P and rectangle Q are similar. Part B Rectangle Q is dilated using a scale factor of 3 to become rectangle R. What are the coordinates of the vertices for rectangle R? Part C The vertices of rectangle S are located at points and Is rectangle S congruent to rectangle P? Explain your answer. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 11
12 14. Rectangle A is shown on the coordinate grid. Unit One Test (Transparallellines) Part A Rectangle A is dilated by a factor of 0.5 about the center point The new rectangle formed is rectangle B. Create a coordinate grid similar to the one shown above. Graph and label rectangle B on the coordinate grid you created. Part B Rectangle B is reflected across the y -axis to form rectangle C. Write the coordinates of each vertex of rectangle C. Explain how the coordinates change when rectangle B is reflected across the y -axis to form rectangle C. Part C Rectangle A is rotated counter-clockwise about the origin to form rectangle D. Graph and label rectangle D on the same coordinate grid you created in Part A. Part D Is rectangle D similar to rectangle B? Explain your answer. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 12
13 15. Roger has a 3-inch-by-5-inch photograph. He is a good painter and wants to make a painting that looks exactly like the photograph but larger. Which one of the following canvases should he buy for this painting? A. 15 inches by 45 inches B. 18 inches by 20 inches C. 24 inches by 40 inches D. 30 inches by 75 inches 16. Susan has two boxes. Each box is 12 cm high, 12 cm long, and 12 cm wide. Which statement describes Susan's boxes? A. The boxes are congruent, but not similar. B. The boxes are similar, but not congruent. C. The boxes are similar and congruent. D. The boxes are only similar. 17. Unit One Test (Transparallellines) Given: ABC ~ DEF. Which statement shown is a correct similarity statement? A. BCA ~ EDF B. BAC ~ EDF C. CBA ~ DFE D. CBA ~ FDE 13
14 18. Line segments PS and QT intersect at point R. Point R is a vertex of right triangle RPQ. Part A What is the measure of angle PQR? Show your work and explain your answer. Part B What is the length of segment RQ? Show your work. Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 14
15 19. Triangles DEF and JKL are shown. Part A What information is provided to show triangle DEF is similar to triangle JKL? Part B What series of transformations could be used to obtain triangle JKL from DEF? Be sure to complete ALL parts of the task. Write your answer and show your work on the paper provided. Do NOT type your answer in the text box below. 15
16 20. A. B. C. D. Permission has been granted for reproduction by the Virginia Department of Education Virginia Department of Education 16
17 Answer Key 1. D) The reflection of line 1 over the x -axis and the reflection of line 2 over the line A) dilation A) circles 7. B) S 8. A) CM and SV 9. C) 10. A) 11. B) ( 4, 2) 12. B) 1 and C) 24 inches by 40 inches 16. C) The boxes are similar and congruent. 17. B) BAC ~ EDF D) 17
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