Rotation of 90 Degrees Clockwise

Rotation of 90 Degrees Clockwise

How to find the image under the rotation of 90 degrees clockwise about the origin: formula, example, and its solution.

Formula

The image of a point (x, y), whose image is under the rotation of 90 degrees clockwise about the origin, is (y, -x).

The image of a point (x, y)
under the rotation of
90º clockwise about the origin
is (y, -x).

Example

Graph the given triangle and its image under the rotation of 90 degrees clockwise about the origin on the coordinate plane. Triangle ABC with vertices A(2, 1), B(5, 4), and C(4, -1)

The image of A(2, 1) is,
y, 1 comma, -x, -2.

So A'(1, -2).

The image of B(5, 4) is,
y, 4 comma, -x, -5.

So B'(4, -5).

The image of C(4, -1) is,
y, -1 comma, -x, -4.

So C'(-1, -4).

ABC has vertices
A(2, 1), B(5, 4), and C(4, -1).

A'B'C' has vertices
A'(1, -2), B'(4, -5), and C'(-1, -4).

Use these vertices
to draw △ABC and its image △A'B'C'
on the coordinate plane.

As you can see,
A'B'C' is under the rotation of
90º clockwise about the origin.

The triangle is only rotated.
There's no change in its size.

So, under a rotation,
the length and the area are reserved.