Matrices in Geometric Transformation

By using matrix addition, we can translate the vertices of a figure.
EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2), translate the preimage 5 units right and 3 units down

A dilation can be done by multiplying the matrix by a factor
EXAMPLE: Given triangle ABC where A (–2,0), B (0, 4) and C (2, 1) Increase the size of the triangle by a factor of 1.5

We can use matrix multiplication to graph reflections in the coordinate plane.
Matrices for Reflections in the Coordinate Plane
Reflection in the y-axis
Reflection in the x-axis
Reflection in the line y = x
Reflection in the line y = –x

EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2),. Reflect the triangle across the y-axis

You can rotate a figure as much as 360 degrees using matrix multiplication
Matrices for Rotations in the Coordinate Plane
Rotation of 90°
Rotation of 180°
Rotation of 270°
Rotation of 360°

EXAMPLE: Given triangle ABC where A (–4, 1), B (– 2, 5) and C (0, 2),. Rotate the triangle 270°

Reference: http://www.jcoffman.com/Algebra2/ch4_4.htm