AMSCO'S Geometry. New York - Rye High School

For each figure, construct the reflection in the given line.a. Segment AB with vertices A(4, 2) and B(2, 4), and line k through points C(2, 1) and D(0, 5).b. Angle EFG with vertices E(4, 3), F(1, 6), and G(6, 6), and line l through points H(1, 3) and I(3, 1).c. Triangle JKL with vertices J(2, 2), K(5, 1), and L(1, 4), and line p through pointsM(7, 3) and N(2, 0).d. Segments PQ and RS with vertices P(3, 4), Q(3, 2), R(1, 0), and S(1, 6), and line q throughpoints T(0, 3) and U(3, 0).Hands-On Activity 2In each figure, one is the image of the other under a reflection in a line. For each figure, constructthe reflection line using a compass and a straightedge.a. Ab. BAAPoint Reflections in the Coordinate Plane 227c. Triangle ABC with vertices A(1, 4), B(4, 3), and (2, 8), and triangle ABC with verticesA(3, 2), B(2, 3), C(7, 3).d. Triangle ABC with vertices A(0, 4), B(7, 1), and C(6, 6), and triangle ABC with verticesA(7, 3), B(4, 4), C(9, 3).6-4 POINT REFLECTIONS IN THE COORDINATE PLANEThe figure at the right illustrates another typeof reflection, a reflection in a point. In the figure,ABC is the image of ABC under areflection in point P. If a line segment is drawnconnecting any point to its image, then thepoint of reflection is the midpoint of that segment.In the figure:• Point A is on AP g, AP PA, and P is themidpoint of AAr.• Point B is on BP g, BP PB, and P is the midpoint of BBr.• Point C is on CP g, CP PC, and P is the midpoint of CCr.ACPBDEFINITIONA point reflection in P is a transformation of the plane such that:1. If point A is not point P, then the image of A is A and P the midpoint of AAr.2. The point P is its own image.