Reflection in the x-axis Matrix

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 and the vertex matrix.

The reflection in the x-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

Triangle ABC has vertices A(1, 2), B(5, 4), and C(3, 1). Its image is under a reflection in the x-axis. Find the coordinates of the vertices of the image.

Previously, you've solved this example.

Reflection in the x-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 x-axis.