# Reflection in the *x*-axis

How to find the image under the reflection in the *x*-axis: formula, example, and its solution.

## Formula

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

under the reflection in the *x*-axis is

(*x*, -*y*).

To find the image,

change the sign of the *y* value.

## Example

To find the image

under the reflection in the *x*-axis,

change the sign of the *y* value.

The image of *A*(-4, 2) is*A*'(-4, -2).

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

change the sign of the *y* value,*B*'(5, -4).

The image of *C*(3, -1) is,

change the sign of the *y* value,*C*'(3, 1).

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

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

The triangle is only filped.

There's no change in its size.

So, under a reflection,

not only in the *x*-axis,

the length and the area are reserved.