# 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

[1 0 / 0 -1].

To find the coordinates of the image,

multiply the reflection matrix [0 1 / 1 0]

in front of the vertex matrix.

Reflection in the line *y* = *x*

Multiplying matrices

## Example

Previously, you've solved this example.

Reflection in the line *y* = *x*

Let's solve the same example

by using the reflection in *y* = *x* matrix.*A*(6, 4), *B*(7, 1), *C*(2, -2)

So the vertex matrix is

[6 7 2 / 4 1 -2].

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

[0 1 / 1 0].

So multiply the reflection matrix [0 1 / 1 0]

in front of the vertex matrix [6 7 2 / 4 1 -2].

Multiply these two matrices.

Multiplying matrices

[Row 1]⋅[Column 1]: 0⋅6 + 1⋅4

[Row 1]⋅[Column 2]: 0⋅7 + 1⋅1

[Row 1]⋅[Column 3]: 0⋅2 + 1⋅(-2)

[Row 2]⋅[Column 1]: 1⋅6 + 0⋅4

[Row 2]⋅[Column 2]: 1⋅7 + 0⋅1

[Row 2]⋅[Column 3]: 1⋅2 + 0⋅(-2)

Then the vertex matrix of the image is

[4 1 -2 / 6 7 2].

The first column is [4 / 6].

So *A*'(4, 6).

The second column is [1 / 7].

So *B*'(1, 7).

The third column is [-2 / 2].

So *C*'(-2, 2).

These are the coordinates of the image.

Here's what you've solved.

By multiplying

the reflection in *y* = *x* matrix [0 1 / 1 0],

you found the vertices of the image (△*A*'*B*'*C*')

under the reflection in *y* = *x*.