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.