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

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

## Matrix

The reflection in the line *y* = *x* matrix is

[0 1 / 1 0].

To find the coordinates of the image,

multiply the reflection matrix and the vertex matrix:

[0 1 / 1 0][*x* / *y*] = [0 + *y* / *x* + 0] = [*y* / *x*].

## Example

Previously, you've solved this example.

Reflection in the line *y* = *x*

Let's solve the same example

by using the reflection matrix.

Multiply the reflection matrix and the vertex matrix:

[0 1 / 1 0][4 7 5 / 1 3 -2] = [1 3 -2 / 4 7 5].

Then the vertices of the image are*A*'(1, 4), *B*'(3, 7), *C*'(-2, 5).

You can see that

by multiplying the reflection matrix, [0 1 / 1 0],

you can find the vertices of the image,

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