Rotation Matrix: 90 Degrees Clockwise

How to use the rotation 90 degrees clockwise matrix to find the image under the rotation: formula, 1 example, and its solution.

Formula

Formula

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

Example

Example

Solution

The image is under
the rotation of 90º clockwise
about the origin.

So write the rotation matrix
[0 1 / -1 0].

Write the vertex matrix.

A(2, 1), B(3, 4), C(5, 3)

So the vertex matrix is
[2 3 5 / 1 4 3].

So the vertex matrix of the image is
[0 1 / -1 0][2 3 5 / 1 4 3].

Solve [0 1 / -1 0][2 3 5 / 1 4 3].

Multiply Matrices

Row 1, column 1:
0⋅2 + 1⋅1

Row 1, column 2:
0⋅3 + 1⋅4

Row 1, column 3:
0⋅5 + 1⋅3

Row 2, column 1:
-1⋅2 + 0⋅1

Row 2, column 2:
-1⋅3 + 0⋅4

Row 2, column 3:
-1⋅5 + 0⋅3

This is the vertex matrix of the image.

0⋅2 + 1⋅1
= 0 + 1

0⋅3 + 1⋅4
= 0 + 4

0⋅5 + 1⋅3
= 0 + 3

-1⋅2 + 0⋅1
= -2 + 0

-1⋅3 + 0⋅4
= -3 + 0

-1⋅5 + 0⋅3
= -5 + 0

0 + 1 = 1

0 + 4 = 4

0 + 3 = 3

-2 + 0 = -2

-3 + 0 = -3

-5 + 0 = -5

[1 4 3 / -2 -3 -5]
is the vertex matrix of the image.

So column 1 is the image of A:
A'(1, -2).

Column 2 is the image of B:
B'(4, -3).

Column 3 is the image of C:
C'(3, -5).

So
A'(1, -2)
B'(4, -3)
C'(3, -5)
is the answer.

Graph

This is the graph of △ABC
and its image △A'B'C'.

The image is under
the rotation of 90º clockwise
about the origin.