Name: Date: Period: Score: Linear Algebra Chapters 7, 8, & 9 Study Guide
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1 1. Triangle ABC is shown on the coordinate grid. 3. Use the parallelogram shown in the coordinate plane to answer each question. Translate 3 units horizontally. Label the image. How are the values in the ordered pairs affected by the translation? Reflect parallelogram GHIJ over the y-axis. What do you notice about the ordered pairs of the original figure and the ordered pairs of its reflection over the y-axis? Translate -5 units vertically. Label the image. How are the values in the ordered pairs affected by the translation? 4. Each equation shown is a result of a translation performed on the equation y = x. Describe the translation. 2. Rotate rectangle PQRS 90 degrees clockwise around the origin. Label the rotation. 5. Each equation shown is a result of a translation performed on the equation. Describe the translation.
2 6. Regina drew a triangle with vertices at (1, 2), (3, 3), and (4, 1). She slides the triangle 2 units down to create an image. What are the vertices of the image? 10. The graph shown is the result of which translation on the equation y = x? (1, 0), (3, 1), and (4, -1) (1, 4), (3, 5), and (4, 3) c. (-1, 2), (1, 3), and (2, 1) d. (3,2), (5,3), and (6,1) 7. Blake drew square ABCD. Then, he drew the image of it, square, 2 centimeters to the right of the original figure. Line segment BC is 3 centimeters. How long is? 1 cm 3 cm c. 5 cm d. 6 cm 8. Bertha drew with the coordinates (4, 2), (5, 3), and (6, 2). Then, she drew an image of this triangle with coordinates (4, -2), (5, -3), and (6, -2). What is the line of reflection for this image? the y-axis the line y = 1 c. the x-axis d. the line x = 1 9. What is the point of rotation? Either a slide to the right 2 units or a slide down 2 units. Either a slide to the left 2 units or a slide down 2 units. c. Either a slide to the right 2 units or a slide up 2 units. d. Either a slide to the left 2 units or a slide up 2 units. 11. Dianne drew a triangle with coordinates (1, 3), (3, 2), and (4, 2). She drew an image of the triangle with coordinates (-1, 3), (-3, 2), and (-4, 2). How did she make the image? She translated the original figure 2 units down. She translated the original figure 6 units down. c. She reflected the original figure over the x- axis. d. She reflected the original figure over the y- axis. Point O Point P c. Point F d. Point E 12. Tasha traces her protractor on a piece of graph paper. Then, she holds one corner of the protractor still while she turns the rest of the protractor 30 degree clockwise. Finally, she traces the protractor again. What type of transformation did Tasha perform? duplication translation c. reflection d. rotation
3 13. Consider the congruence statement. 17. statement might not be true? Identify the congruent sides. Identify the congruent angles. c. The length of is equal to the length of. d. The distance between points R and T is equal to the distance between points U and W 14. For the figure shown, which is a correct congruence statement? 18. Which transformation was used to create from? ABC BCD ACB BDC c. ABC DCB d. CAB CBD 15. If, which congruence statement must be true? c. d. was reflected over the y-axis was translated to the right 3 units and down 1 unit c. was rotated 90 degrees clockwise about the origin d. was translated to the right 1 unit and down 3 units. 16. If the point (-5, 8) is rotated 90 degrees counterclockwise about the origin, what will be the coordinates of the rotated point? (5, -8) (-8, 5) c. (5, 8) d. (-8, -5)
4 19. Suppose that. Identify the corresponding angles. 21. Triangle FUN has vertices with coordinates F(-2, 4), U(-6, -4), and N(6, 0). Dilate using the origin as the center of dilation and a scale factor of 0.5 to form. State the relationships between the corresponding angles. c. Identify the corresponding sides. What are the coordinates of the image? d. State the relationship between lengths of the corresponding sides. c. How did you determine the coordinates of the vertices of the dilated image? e. Determine the lengths of and if centimeters, centimeters, centimeters, and centimeters. d. Is the dilation an enlargement or a reduction? Explain your reasoning. e. What is the relationship between and? 20. A triangle has vertices at (1, 1), (1, 2), and (3, 2). It is dilated by a scale factor of 4 with the origin as the center of dilation to form a similar triangle. What are the coordinates of the vertices of the image? (4, 1), (4, 2), (6, 2) (1, 4), (1, 5), (3, 5) c. (4, 4), (4, 8), (12, 8) d. (3, 3), (3, 6), (9, 6) 22. Which must be true of a scale factor of a dilation if the image is larger than the original figure? The scale factor is positive. The scale factor is between -1 and 0. c. The scale factor is between 0 and 1. d. The scale factor is greater than 1.
5 23. Triangle A B C is the image that resulted from a dilation of triangle ABC. 25. Given APZ ~ DPE Which is the length of EP? Which point is the center of dilation? (0, 0) A c. C d. B 24. In the figure,. What is the length of? 15 cm 10 cm c. 13 cm d. 9 cm 26. A triangle is dilated with a center of dilation at the origin. Point P is on the figure and is the corresponding point on the image of the dilation. Point P is at (-2, 3) and is at (-8, 12). What is the scale factor? 2 4 c. 6 d Which is not a correct conclusion? 3.6 centimeters 9.6 centimeters c. 6 centimeters d. 7 centimeters c. d.
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