Geometry Lesson 6.2B – Reflections and Rotations CGT.5.G.5 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane translations reflections rotations (90˚, 180˚, clockwise and counterclockwise about the origin) dilations (scale factor)

Transformations A transformation of a geometric figure is a change in its position, shape, size, or orientation. A transformation describes, or maps, a change from one figure to another. The original figure is a pre-image. The resulting figure is an image.

Reflection across the y-axis B C A’ B’ C’ Reflection across the y-axis Preimage Points: A(-2,1) B(-7,3) C(-3,8) Image Points:

Reflection across the y-axis Preimage Points: A(7,-7) B(3,-1) C(9,-3) Image Points: Reflection across the y-axis B’ A’ C’ B A C

Reflection across the x-axis B C Reflection across the x-axis A’ B’ C’ Preimage Points: A(-2,1) B(-7,3) C(-3,8) Image Points:

Point Reflection (2, 1) (-2, -1) (7, 3) (-7, -3) (3, 8) (-3, -8) Reflection across y-axis x-axis A(-2,1) B(-7,3) C(-3,8) ( x , y ) (2, 1) (-2, -1) (7, 3) (-7, -3) (3, 8) (-3, -8) (-x, y) (x, -y)

Graph the lines y = x and y = -x and reflect: A(3,8) B(3,5) C(-2,5) over both

Reflecting Across the Lines y = x and y = -x. The reflection of the point (x,y) across the line y = x is the point (y,x). The reflection of the point (x,y) across the line y = -x is the point (-y,-x).

Reflections in Use The gas company needs to place a meter on their gas line and run pipes to your and your neighbor’s houses. Where should they install in order to run the least amount of pipe? Gas Line Your House Neighbor’s

Reflections in Use Gas Line Your House Neighbor’s House

Rotations A rotation spins a figure around a point. In this class, we will always rotate around the origin. Rotation can either be clockwise (CW) or counter-clockwise (CCW)

Point Rotations 90o counterclockwise (CCW) maps (x, y) to (-y, x) With the center at the origin: 90o counterclockwise (CCW) maps (x, y) to (-y, x) 90o clockwise (CW) maps (x, y) to (y, -x) 180o maps (x, y) to (-x, -y)

Points in Rotation (-1,- 2) (1, 2) (2, -1) (-3, -7) (3, 7) (7, -3) 90○ CCW 90○ CW 180○ A(-2,1) B(-7,3) C(-3,8) (-1,- 2) (1, 2) (2, -1) (-3, -7) (3, 7) (7, -3) (-8, -3) (8, 3) (3, -8)

Rotation Around the Origin 90o CW 90o CCW 180o

Mr. York’s Hints for Rotating Shapes To rotate a figure 90o: rotate your paper, notice where the vertices rotated to, rotate back and plot vertices. To rotate a figure 180o , turn your paper upside down. Graph the points from the original shape.