Reflection in the y-axis Matrix

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.

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

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

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.