This document discusses using matrices to perform reflections of geometric figures. Reflection matrices are special 2x2 matrices that can reflect vertices expressed as a matrix over lines like the x-axis, y-axis, and y = -x. The document provides examples of reflection matrices for common lines and instructs the reader to reflect a sample image over the line y = -x using the appropriate reflection matrix, as well as perform all four basic reflections.

1. Ch.8.7_Reflections.notebook March 05, 2012
Chapter 8.7
Reflections Using Matrices
What are the coordinates
of the vertices?
Express the vertices as a matrix
We can perform reflections using special
2x2 matrices and vertex matrices
Reflection Matrices
over y = x
over x­axis
0 1
1 0
1 0
0 ­1
over y = ­x
over y­axis
0 ­1
­1 0 ­1 0
0 1
Reflect the image above
over the line y = ­x
0 ­1
­1 0
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2. Ch.8.7_Reflections.notebook March 05, 2012
Perform all 4 reflections
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3. Ch.8.7_Reflections.notebook March 05, 2012
Page 370
1 ­ 14
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