1. 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)

2. 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.

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

4. 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

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

6. 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)

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

8. 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).

9. 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

10. Reflections in Use
Gas Line
Your
House
Neighbor’s
House

11. 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)

12. 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)

13. 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)

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

15. 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.