# Reflection in the Line *y* = *x*

How to find the image under the reflection in the line *y* = *x*: formula, example, and its solution.

## Formula

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

under the reflection in the line *y* = *x* is

(*y*, *x*).

To find the image,

switch *x* and *y*.

## Example

To find the image

under the reflection in the line *y* = *x*,

switch *x* and *y*.

The image of *A*(6, 4) is*A*'(4, 6).

The image of *B*(7, 1) is,

switch *x* and *y*,*B*'(1, 7).

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

switch *x* and *y*,*C*'(-2, 2).

△*ABC* has vertices*A*(6, 4), *B*(7, 1), and *C*(2, -2).

△*A'B'C'* has vertices*A*'(4, 6), *B*'(1, 7), and *C*'(-2, 2).

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 line *y* = *x*.

The triangle is only filped.

There's no change in its size.

So, under a reflection,

not only in the line *y* = *x*,

the length and the area are reserved.