 # Rotation of 90 Degrees Counterclockwise Matrix How to use the rotation of 90 degrees counterclockwise matrix to find the image under the reflection: the matrix, example, and its solution.

## Matrix The rotation of 90º counterclockwise 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 counterclockwise

Multiplying matrices

## Example Previously, you've solved this example.

Rotation of 90º counterclockwise

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