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Unit: Transformational Geometry Name ____________________________ Assessment Review Period ___________ Date ____________ G.CO.2 Learning Target: I can describe a transformation using coordinate notation that maps one point onto a unique image point. I can compare transformations that preserve distance and angle to those that do not. 1. Translate the quadrilateral , , 3. ∆JKL is rotated 90° clockwise about the origin and then translated using . What are the coordinates of the final image of point L under this composition of transformations? , using the transformation ( x, y ) ( x 2, y 3) . A. B. , , C. D. , , , , , , , , , , Answer:_____________________________ 2. After a translation, the image is . Identify the image of the point Q after this same translation. Then, describe the rule of the rigid transformation in coordinate notation and in words. 4. ∆ABC is translated using ( x, y ) ( x 1, y 3) after it is reflected across the y-axis. What are the coordinates of the final image of point C under this composition of transformations? y Point Q’:__________________ 4 Coordinate notation: 2 A ______________________________________ Words: –4 –2 B 2 x 4 –2 ______________________________________ C –4 Answer:_____________________________ 5. A triangle with vertices , , and is rotated 180 degrees clockwise about the point (-2, 1). Graph and label the pre-image and the image. G-CO.3: I can demonstrate the rotations and reflections that carry a rectangle, parallelogram, trapezoid, or regular polygon onto itself. 7. Complete the given chart given that you are referencing REGULAR polygons: Sides Lines of Symmetry Degrees of Rotational Symmetry 3 4 5 6 7 Answer:_____________________________ 8 6. What are the endpoints of the image is reflected about the line ? if n 8. What rotation will map the figure onto itself? A. B. C. D. A. B. C. D. about the center about the center about the center from the top 9. What is the angle of rotation that maps the equilateral triangle onto itself? 11. Marta is studying the symmetry of a regular pentagon drawn on a piece of paper. C B A Describe all the ways you can map A onto B? Marta tried folding the paper along a vertical line and horizontal line as shown below and concluded that a regular pentagon has only 1 line of symmetry. Fold Fold 10. Sketch a hexagon that has a line of symmetry at y = -x + 5 below: She then turned the paper upside down and noted that the figure no longer looks the same. She concluded a regular pentagon has no rotational symmetry. A. Explain the flaws in Marta’s reasoning and describe the true symmetry of the figure. _________________________________ _________________________________ B. What is the smallest angle of rotation that the figure maps onto itself? _________________________________ G-CO.4: I can develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 12. Identify a single transformation that is equivalent to reflecting the figure across line n and then reflecting that image across line m. 15. Given the figure below. Part A: Is to a congruence transformation? Explain. Answer:_____________________________ _________________________________ 13. What angle of rotation maps to ? _________________________________ Part B: Is to a rotation? Explain. _________________________________ _________________________________ Part C: Use coordinate notation to describe the translation to . A. B. C. D. 14. . Which mapping represents a rotation of clockwise about the origin? A. B. C. D. _________________________________ _________________________________ 16. Cassie claims the transformation rule rotates figures 180 degrees 18. The vertices of are , and about the origin. Plot , the triangle generated by this rule, and discuss whether Cassie is correct. . Find the vertices of after a composition of the transformation in the order they are listed. y Translation: 6 C Reflection: in the -axis 5 4 3 2 1 –6 –5 –4 –3 –2 –1 –1 O B 1 2 A 3 4 5 6 x –2 –3 –4 –5 –6 Answer: ____________________________________ Answer:_____________________________ ____________________________________ 19. When produce ___________________________________ 17. If a point not on a given vertical line is reflected over said line, then the point and its image will ______________________. a. be on the same vertical line. b. be on the same horizontal line. c. Both A and B d. Neither A and B is reflected over to , which statement will not necessarily be true? A. B. C. D. G-CO.6: I can decide if two shapes are congruent because of the rigid motions between the two figures. I can investigate rigid motions and generalize their characteristics as preserving congruence. I can find a sequence of transformations that will carry a shape onto another. G-CO.5: I can demonstrate and draw transformations. I can find a sequence of transformations that will carry a shape onto another 20. with vertices , , and is reflected across the y-axis, and then its image is reflected across the line . P(–6, 1), Q(–5, 4), R(–2, 5), and S(–3, 2), Which single transformation moves the triangle from its starting position to its final position? A. B. C. D. was reflected over the line x = –1. Liam states that the reflection of PQRS must also be a rhombus because a reflection is a congruence transformation. Explain what Liam means by this statement. rotation by about the origin rotation by about the origin reflection across the x-axis reflection across the y-axis 21. Ann wants to create a design to decorate her Geometry binder. She reflects part of the design across line p and then reflects the image across line n. Describe a single transformation that moves the part of the design from its starting position to its final position. p Answer: ____________________________________ ____________________________________ ___________________________________ Start n Finish A. B. C. D. 22. Rhombus PQRS, with vertex coordinates rotation of 180° about the origin rotation of 90° about the origin translation along the line reflection across the line 23. Determine whether triangles are congruent. Explain. 24. Suvi was given triangle ABC such that A(9, 1), B (5, 3) and C (7, -4). He then was asked to reflected it over the x-axis and translate it up 5 units. His answer was that the new coordinates of the transformation would be A’’(9, 4), B’’(-5, 8) and C’’(7, 9). After verifying by graphing his answer he saw he was incorrect. What did Suvi do incorrect, and correct his mistake. and y 6 G –6 E F P Q 6 R –6 A. The triangles are congruent because can be mapped to by a reflection: . B. The triangles are congruent because can be mapped to by a rotation: . C. The triangles are congruent because can be mapped to by a reflection: . D. The triangles are congruent because can be mapped to by a rotation: . x