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 in front of 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 [1 0 / 0 -1]
in front of the vertex matrix.

Reflection in the x-axis

Multiplying matrices

Example

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

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.