Reflection Matrix in 2D

Here is a simple setup of a manipulation and reflection matrix in 2D space.
By using a reflection matrix, we can determine the coordinates of the point , the reflected image of the point in the line defined by the vector from the origin.
The projection of onto the line is . The point is then determined by extending the segment by . As vectors, .
If is normalized (so that , the reflection matrix is . Then , that is, the reflection of a reflection is the identity. Also, .


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Related Curriculum Standards

US Common Core State Standards, Mathematics