# Reflection in the Origin

How to find the image under the reflection in the origin: formula, example, and its solution.

## Formula

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

under the reflection in the origin is

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

To find the image,

change the signs of both *x* and *y* values.

## Example

To find the image

under the reflection in the origin,

change the signs of both *x* and *y* values.

The image of *A*(-3, 5) is*A*'(3, -5).

The image of *B*(5, 4) is,

change the signs of both *x* and *y* values,*B*'(-5, -4).

The image of *C*(2, -1) is,

change the signs of both *x* and *y* values,*C*'(-2, 1).

△*ABC* has vertices*A*(-3, 5), *B*(5, 4), and *C*(2, -1).

△*A'B'C'* has vertices*A*'(3, -5), *B*'(-5, -4), and *C*'(-2, -1).

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 reflection in the origin.

The triangle is only filped.

There's no change in its size.

So, under a reflection,

not only in the origin,

the length and the area are reserved.