# Reflection Matrix: Origin

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

## Formula

The reflection in the origin matrix is

-I = [-1 0 / 0 -1].

I: Identity matrix

## Example

The image is under

the reflection in the origin.

So write the reflection in the origin matrix

-I.

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

-I[2 3 5 / 1 4 3].

I is the identity matrix.

So, by its definition,

I[2 3 5 / 1 4 3]

= [2 3 5 / 1 4 3].

Multiply minus to each element.

[-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.

This is the graph of △ABC

and its image △A'B'C'.

The image is under

the reflection in the origin.