Geometric Linear Transformations in 2D space

Author:Ku, Yin Bon (Albert)

Geometric Linear Transformations

In this section, we describe some specific linear transformations in

that are geometric in nature. They are as follows:

Rotation about the origin through a given angle
Reflection in a line that passes through the origin
Scaling horizontally or vertically
Horizontal or vertical shear
Projection onto x-axis or y-axis

In the applet, you can see the effect on

under various geometric transformations: First, you select the type of geometric linear transformation

. Second, you click the "Set" button to set up the corresponding

and

and the matrix for

. Then click the "Go" button to see how the triangle is transformed under

What is the general form of the matrix for the rotation about the origin through angle in the counterclockwise direction?

Find the matrix for the 2D linear transformation that first rotates about the origin through in the counterclockwise direction and then reflect on the y-axis.

Geometric Linear Transformations in 2D space

Geometric Linear Transformations

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