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NAME__________________________________________ GEOMETRY TRANSFORMATIONS 1. 2. If point (7,-1) is reflected over the y-axis, the image is (1) (-7,-1) (2) (-7,1) ______DATE______ ______ MRS. BINASO (3) (-1,7) (4) (-1,-7) In the accompanying diagram, which circle is the image of circle O after a reflection in the x-axis? Y X (1) O 3. (2) O' (3) O" (4) O''' When point P(-3,5) is reflected over the line x = 1, the image is (1) (5,-3) (2) (3,5) (3) (4,5) (4) (5,5) 4. Line segment PQ has coordinates P(-3,2) and Q(a,b) as its endpoints. If its image P'Q' after being reflected in the line y = x has endpoints P'(c,d) and Q'(7,4) find the values of a, b, c, and d. 5. If the line whose equation is y = x 4 is reflected first over the y-axis and then over the x-axis. Find the equation of the resulting image. 6. The letter A has: (1) line symmetry only (2) point symmetry only (3) line and point symmetry (4) no symmetry Which figure has exactly one line of symmetry? (1) equilateral triangle (2) regular hexagon (3) isosceles triangle 7. 8. 9. Circle each of the letters that have only one line of symmetry. A B C D E F G L M N O P Q R W X Y Z H S I T (4) rectangle J U K V Identify the letters listed in exercise #8 that have only point symmetry. 10. The image of A(2,5) under a reflection in point P is A'(4,-3). Find the coordinates of P. (1) (3,1) (2) (6,2) (3) (-.5,4.5) (4) (3,4) 11. If the point B(-3,5) is reflected in point P(2,3), find the coordinates of B'. 12. The image of A(3,-1) under a reflection in a point P is A'(-5,5). Find B' the image of B(4,-2) under a reflection in P. 13. If a translation moves A(1,4) to A'(4,6), what will be the coordinates of B', the image of B(-2,3)? (1) (1,5) (2) (-5,5) (3) (-8,4.5) (4) (1,3) 14. A translation moves P(2,4) to P'(0,0). What would the image of Q(4,2) be under the same translation? (1) (0,0) (2) (2,4) (3) (2,-2) (4) (8,2) 15. If a translation maps A(3,4) onto A'(2,5), what would be coordinates of the image of A' under the same translation? 16. Which translation maps (1,-2) (-10,14)? (1) (x9, y+12) (2) (x11, y+16) (3) (x10, y+14) (4) (x11, y+12) 17. If a translation T1,-2 maps (x,6) onto (-4,4), what is the value of x? 18. Under a dilation with respect to the origin, the image of A(2,3) is A'(10,15). What are the coordinates of B', the image of (1,4), under the same dilation? (1) (9,16) (2) (16,9) (3) (5,20) (4) (20,5) 19. If a dilation maps (10,-6) onto (x,-3), what is the value of x? (1) 7 (2) 5 (3) 13 20. Which of the following transformations is a dilation? (1) P(4,2) P'(6,4) (2) P(4,2) P'(2,1) (3) P(4,2) (4) P(4,2) 21. Which dilation maps (-3,5) (1) D6 (3) D.5 (6,-10)? (2) D2 (4) -5 P'(4,-2) P'(2,-1) (4) D18 22. If a translation moves A(-1,2) to A'(-2,-3), the rule of translation would be (1) one unit right, five units down (3) one unit left, five units down (2) three units left, one unit down (4) two units right, six units down 23. A line segment with endpoints (1,-5) and (0,4) is reflected about a line and the new endpoints are (-5,1) and (4,0). The reflection must have taken place about the (1) x-axis (2) y-axis (3) the line y = x (4) the origin 24. If the line whose equation is y = x + 2 is reflected over the y-axis, its image would have the equation (1) y = -x + 2 (2) y = -x 2 (3) x = y + 2 (4) y = 2x 25. If a dilation maps (2,5) onto (14,y), what is the value of y? 26. B(2,2) has an image B' after being reflected about the y-axis. If B' undergoes a dilation of 3 with respect to the origin, the new image is (1) (6,6) (2) (-6,6) (3) (6,-6) (4) none of these