# 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 90º clockwise matrix is
[0 1 / -1 0].

To find the coordinates of the image,
multiply the rotation matrix [0 1 / -1 0]
in front of the vertex matrix.

Rotation of 90º clockwise

Multiplying matrices

## Example

Previously, you've solved this example.

Rotation of 90º clockwise

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

A(2, 1), B(5, 4), C(4, -1)

So the vertex matrix is
[2 5 4 / 1 4 -1].

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

So multiply the rotation matrix [0 1 / -1 0]
in front of the vertex matrix [2 5 4 / 1 4 -1].

Multiply these two matrices.

Multiplying matrices

[Row 1]⋅[Column 1]: 0⋅2 + 1⋅1
[Row 1]⋅[Column 2]: 0⋅5 + 1⋅4
[Row 1]⋅[Column 3]: 0⋅4 + 1⋅(-1)

[Row 2]⋅[Column 1]: (-1)⋅2 + 0⋅1
[Row 2]⋅[Column 2]: (-1)⋅5 + 0⋅4
[Row 2]⋅[Column 3]: (-1)⋅4 + 0⋅(-1)

Then the vertex matrix of the image is
[1 4 -1 / -2 -5 -4].

The first column is [1 / -2].
So A'(1, -2).

The second column is [4 / -5].
So B'(4, -5).

The third column is [-1 / -4].
So C'(-1, -4).

These are the coordinates of the image.

Here's what you've solved.

By multiplying
the rotation of 90º clockwise matrix [0 1 / -1 0],
you found the vertices of the image (△A'B'C')
under the rotation of 90º counterclockwise.