# 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).