Rotation: 90 Degrees Counterclockwise

How to find the image under the rotation of 90 degrees counterclockwise about the origin: formula, 2 examples, and their solutions.

Formula

Formula

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

Switch x and y.
and change the sign of y.

Example 1

Example

Solution

The image of (3, 2) is
under the rotation of
90º counterclockwise about the origin.

Then the image point is,

switch x and y,
(2, 3),

and change the sign of y,
(-2, 3).

So (-2, 3) is the answer.

Graph

This is the graph of (3, 2)
and its image
under the rotation
90º counterclockwise about the origin:
(-2, 3).

Example 2

Example

Solution

The image of (-4, -5) is
under the rotation of
90º counterclockwise about the origin.

Then the image point is,

switch x and y,
(-5, -4),

and change the sign of y,
(5, -4).

so (5, -4) is the answer.

Graph

This is the graph of (-4, -5)
and its image
under the rotation
90º counterclockwise about the origin:
(5, -4).