# Rotation of 90 Degrees Counterclockwise

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

## Formula

The image of a point (*x*, *y*)

under the rotation of

90º counterclockwise about the origin

is (-*y*, *x*).

## Example

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 counterclockwise 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.