# Reflection Matrix: y-axis

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

## Formula

### Formula

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

## Example

### Solution

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

So write the reflection in the y-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)