Rotation of 90 Degrees Clockwise Matrix

Rotation of 90 Degrees Clockwise Matrix

How to use the rotation of 90 degrees clockwise matrix to find the image under the reflection: the matrix, example, and its solution.

Matrix

The rotation of 90 degrees clockwise matrix is [0 1 / -1 0]. To find the coordinates of the image, multiply the rotation matrix and the vertex matrix.

The rotation of 90º clockwise matrix is
[0 1 / -1 0].

To find the coordinates of the image,
multiply the reflection matrix and the vertex matrix:
[0 1 / -1 0][x / y] = [0 + y / -x + 0] = [y / -x].

Example

Triangle ABC has vertices A(1, 2), B(5, 4), and C(3, 1). Its image is under a rotation of 90 degrees clockwise about the origin. Find the coordinates of the vertices of the image.

Previously, you've solved this example.

Rotation of 90º clockwise

Let's solve the same example
by using the reflection matrix.

Multiply the reflection matrix and the vertex matrix:
[0 1 / -1 0][1 5 3 / 2 4 1] = [2 4 1 / -1 -5 -3].

Then the vertices of the image are
A'(2, -1), B'(4, -5), C'(1, -3).

You can see that
by multiplying the rotation matrix, [0 1 / -1 0],
you can find the vertices of the image,
which is under the rotation of 90º clockwise.