# Reflection in the *y*-axis Matrix

How to use the reflection in the *y*-axis matrix to find the image under the reflection: the matrix, example, and its solution.

## Matrix

The reflection in the *y*-axis matrix is

[-1 0 / 0 1].

To find the coordinates of the image,

multiply the reflection matrix and the vertex matrix:

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

## Example

Previously, you've solved this example.

Reflection in the *y*-axis

Let's solve the same example

by using the reflection matrix.

Multiply the reflection matrix and the vertex matrix:

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

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

You can see that

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

you can find the vertices of the image,

which is under the reflection in the *y*-axis.