# Reflection in the *x*-axis Matrix

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

## Matrix

The reflection in the *x*-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 *x*-axis

Multiplying matrices

## Example

Previously, you've solved this example.

Reflection in the *x*-axis

Let's solve the same example

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

So the vertex matrix is

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

The reflection in the *x*-axis matrix is

[1 0 / 0 -1].

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

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

Multiply these two matrices.

Multiplying matrices

[Row 1]⋅[Column 1]: 1⋅(-4) + 0⋅2

[Row 1]⋅[Column 2]: 1⋅5 + 0⋅4

[Row 1]⋅[Column 3]: 1⋅3 + 0⋅(-1)

[Row 2]⋅[Column 1]: 0⋅(-4) + (-1)⋅2

[Row 2]⋅[Column 2]: 0⋅5 + (-1)⋅4

[Row 2]⋅[Column 3]: 0⋅3 + (-1)⋅(-1)

Then the vertex matrix of the image is

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

The first column is [-4 / -2].

So *A*'(-4, -2).

The second column is [5 / -4].

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

The third column is [3 / 1].

So *C*'(3, 1).

These are the coordinates of the image.

Here's what you've solved.

By multiplying

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

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

under the reflection in the *x*-axis.