AMSCO'S Geometry. New York - Rye High School

226 Transformations and the Coordinate PlaneDeveloping SkillsIn 3–7: a. On graph paper, locate each point and its image under r x-axis. b. Write the coordinates ofthe image point.3. (2, 5) 4. (1, 3) 5. (2, 3) 6. (2, 4) 7. (0, 2)In 8–12: a. On graph paper, locate each point and its image under r y-axis. b. Write the coordinates ofthe image point.8. (3, 5) 9. (1, 4) 10. (2, 3) 11. (2, 3) 12. (1, 0)In 13–17: a. On graph paper, locate each point and its image under r yx. b. Write the coordinates ofthe image point.13. (3, 5) 14. (3, 5) 15. (4, 2) 16. (1, 5) 17. (2, 2)Applying Skills18. Prove Theorem 6.3, “Under a reflection in the x-axis, the image of P(a, b) is P(a, b).”19. When the points A(4, 0), B(0, 4), C(4, 0) and D(0, 4) are connected in order, squareABCD is drawn.a. Show that the line y = x is a line of symmetry for the square.b. Show that the y-axis is a line of symmetry for the square.20. Show that the y-axis is not a line of symmetry for the rectangle whose vertices are E(0, 3),F(5, 3), G(5, 3), and H(0, 3).21. Write the equation of two lines that are lines of symmetry for the rectangle whose verticesare E(0, 3), F(6, 3), G(6, 3), and H(0, 3).Hands-On Activity 1In this activity, you will learn how to construct a reflection in a line using a compass and astraightedge, or geometry software. (Note: Compass and straightedge constructions can alsobe done on the computer by using only the point, line segment, line, and circle creation toolsof your geometry software and no other software tools.)STEP 1. Draw a line segment. Label the endpoints A and B. Draw a reflection line k.STEP 2. Construct line l perpendicular to line k through point A. Let M be the point where lines land k intersect.STEP 3. Construct line segment ArM congruent to AM along line l. Using point M as the center,draw a circle with radius equal to AM. Let A be the point where the circle intersects linel on the ray that is the opposite ray of MAh.STEP 4. Repeat steps 2 and 3 for point B in order to construct B.STEP 5. Draw ArBr.Result: ArBr is the image of AB under a reflection in line k.