Reflection Matrix: x-axis

How to use the reflection in the x-axis matrix to find the image under the reflection: formula, 1 example, and its solution.

Formula

Formula

The reflection in the x-axis matrix is
[1 0 / 0 -1].

Example

Example

Solution

The image is under
the reflection in the x-axis.

So write the reflection in the x-axis matrix
[1 0 / 0 -1].

Write the vertex matrix.

A(2, 1), B(3, 4), C(5, 3)

So the vertex matrix is
[2 3 5 / 1 4 3].

So the vertex matrix of the image is
[1 0 / 0 -1][2 3 5 / 1 4 3].

Solve [1 0 / 0 -1][2 3 5 / 1 4 3].

Multiply Matrices

Row 1, column 1:
1⋅2 + 0⋅1

Row 1, column 2:
1⋅3 + 0⋅4

Row 1, column 3:
1⋅5 + 0⋅3

Row 2, column 1:
0⋅2 + (-1)⋅1

Row 2, column 2:
0⋅3 + (-1)⋅4

Row 2, column 3:
0⋅5 + (-1)⋅3

This is the vertex matrix of the image.

1⋅2 + 0⋅1
= 2 + 0

1⋅3 + 0⋅4
= 3 + 0

1⋅5 + 0⋅3
= 5 + 0

0⋅2 + (-1)⋅1
= 0 - 1

0⋅3 + (-1)⋅4
= 0 - 4

0⋅5 + (-1)⋅3
= 0 - 3

2 + 0 = 2

3 + 0 = 3

5 + 0 = 5

0 - 1 = -1

0 - 4 = -4

0 - 3 = -3

[2 3 5 / -1 -4 -3]
is the vertex matrix of the image.

So column 1 is the image of A:
A'(2, -1).

Column 2 is the image of B:
B'(3, -4).

Column 3 is the image of C:
C'(5, -3).

So
A'(2, -1)
B'(3, -4)
C'(5, -3)
is the answer.

Graph

This is the graph of △ABC
and its image △A'B'C'.

The image is under
the reflection in the x-axis.