# 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 [-1 0 / 0 1]

in front of the vertex matrix.

Reflection in the *y*-axis

Multiplying matrices

## Example

Previously, you've solved this example.

Reflection in the *y*-axis

Let's solve the same example

by using the reflection in the *y*-axis matrix.*A*(-2, 1), *B*(5, 4), *C*(3, -2)

So the vertex matrix is

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

The reflection in the *y*-axis matrix is

[-1 0 / 0 1].

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

in front of the vertex matrix [-2 5 3 / 1 4 -2].

Multiply these two matrices.

Multiplying matrices

[Row 1]⋅[Column 1]: (-1)⋅(-2) + 0⋅1

[Row 1]⋅[Column 2]: (-1)⋅5 + 0⋅4

[Row 1]⋅[Column 3]: (-1)⋅3 + 0⋅(-2)

[Row 2]⋅[Column 1]: 0⋅(-2) + 1⋅1

[Row 2]⋅[Column 2]: 0⋅5 + 1⋅4

[Row 2]⋅[Column 3]: 0⋅3 + 1⋅(-2)

Then the vertex matrix of the image is

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

The first column is [2 / 1].

So *A*'(2, 1).

The second column is [-5 / 4].

So *B*'(-5, 4).

The third column is [-3 / -2].

So *C*'(-3, -2).

These are the coordinates of the image.

Here's what you've solved.

By multiplying

the reflection in the *y*-axis matrix [-1 0 / 0 1],

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

under the reflection in the *y*-axis.