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Name: Class: Date: REVIEW: Transformations and Congruence Use trapezoid GHIJ. 5. The ordered pair R( 2, 7) is translated 5 units to the right and down 2 units. Use an algebraic representation to describe the translation. 6. Triangle FGH has vertices F(3, 1), G(5, 1), and H(5, 2). What are the coordinates of the image of point H after a translation 1 unit to the right and 3 units down? 1. If the figure is translated 3 units left and 4 units down, what are the coordinates of G' ? 7. Quadrilateral JKLM has vertices J ( 4, 4), K( 4, 1), L(1, 1), and M(1, 4). What are the coordinates of the image of point K after a reflection across the x-axis? 2. If the figure is rotated 90 clockwise about the origin, what are the coordinates of H' ? 3. If the figure is reflected over the y-axis, what are the coordinates of I' ? 8. Write congruence statements comparing the corresponding parts in the congruent quadrilaterals ABCD and EFGH. 4. After a translation, the coordinates of J' are ( 3, 4). Represent the translation algebraically. a. (x, y) (x 3, y 4) b. (x, y) (x 2, y 5) c. (x, y) (x 2, y 4) d. (x, y) (x 3, y 5) Angle Statements: Side Statements: 9. Determine if the two figures shown at the right are congruent by using transformations. Explain your reasoning. 12. Graph and label the image of reflection over the y-axis. YZW after a Transformations: 13. What will be the coordinates of triangle Y' Z' W' if trianlge YZW is reflected across the y-axis and translated 3 units down? Refer to the graph of YZW below. a. Y” (4, 1), Z” ( 4, 1), W” (0, 7) b. Y” (4, 1), Z” ( 4, 1), W” (0, 7) c. Y” (4, 1), Z” ( 4, 1), W” (0, 7) d. Y” (4, 1), Z” ( 4, 1), W” (0, 7) 14. Triangle ABC has vertices A(3, 2), B( 2, 3), and C(1, 3). The triangle is reflected over the x-axis and then translated 2 units left to form triangle A'B'C' . What are the coordinates of A', B' , and C' ? 10. Graph and label the image of YZW after a translation 2 units right and 1 unit down. 11. YZW is translated 2 units right and 1 unit down. Write an algebraic expression to describe the translation. a. (x, y) (x 2, y 1) b. (x, y) (x 2, y + 1) c. (x, y) (x 2, y + 1) d. (x, y) (x 1, y + 2) Page 2 15. Quadrilateral KLMN has vertices K(2, 1), L(5, 2), M(7, 5), N(4, 4). The quadrilateral is rotated 90 clockwise about the origin and then translated 1 unit down. What are the coordinates of the vertices of quadrilateral K'L'M'N' ? 18. If point A is translated 5 units left and 2 units down, what will be the coordinates of point A in its new position? Rotation Steps: Translation Steps: 16. Triangle ABC has vertices , and . Graph the vertices of triangle a translation of 5 units right and 6 units up. after 17. Triangle ABC with vertices A(–3, 2), B(–8, 8), and C(–3, –2) translated 2 units up and 8 units right 19. Construct the reflection over the x-axis of the trapezoid given below: 20. Find the coordinates of the vertices of the figure after a reflection over the x-axis. Then graph the reflection image. 20. x-axis Page 3 21. A rectangle with vertices A(4, –4), B(4, –8), C(6, – 8)and D(6, –4) is rotated 270° clockwise about the origin. 25. Determine if the two figures are congruent by using transformations. 22. A triangle with vertices L(–3, 5), M(–3, 9), and N(–9, 5) is rotated 180° counterclockwise about the origin. 23. Identify the coordinates for the triangle ABC, when it is rotated clockwise about the origin by . a. The figures are congruent because a reflection followed by a rotation will map figure M onto figure N. b. The figures are congruent because a translation followed by a rotation will map figure M onto figure N. c. The figures are congruent because a rotation followed by a translation will map figure M onto figure N. d. The figures are not congruent. No transformations will match the two figures up exactly. 26. In the figure below, NO = 24, and MO = 26, what is LP? . If MN = 10, 24. Triangle XYZ has vertices at (1, 1), (1, 5), and (3, 5). 27. Write congruence statements comparing the corresponding parts in the congruent figures below. a. Translate XYZ 3 units down, then reflect it over the y-axis. Label the vertices of the image X'Y'Z'. b. Find the lengths of the sides of XYZ and X'Y'Z'. c. Are the triangles congruent? Justify your answer. Page 4 Page 5 Answer Key 1. b 28. When reflected across the y-axis, the x-coordinate becomes its opposite. 2. c 3. a 4. b 5. d 6. c 7. b 8. a 9. a (–2, 3), (–4, 1), (–4, –4), (–2, –2) 10. c 29. 11. a 12. b , , , , , , , 30. a. X' (–1, –2), Y' (–1, 2), Z' (–3, 2) 13. c 14. d 15. c 16. b 17. c 18. b 19. d 20. b 21. d 22. c b. XYZ: XY = 4 units, YZ = 2 units, and XZ = units X'Y'Z': X'Y' = 4 units, Y'Z' = 2 units, and X'Z' = units c. Yes; Sample answer: The matching sides are the same length. 23. a 24. b 25. a 26. d 27. c Page 6