Rotation of 90 Degrees Counterclockwise Matrix

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

Triangle ABC has vertices A(2, 1), B(5, 4), and C(4, -1). Triangle A'B'C' is the image of triangle ABC under the rotation of 90 degrees counterclockwise about the origin. Find the coordinates of the vertices of triangle A'B'C'.

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.