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

Formula

The reflection in the origin matrix is
-I = [-1 0 / 0 -1].

I: Identity matrix

Example

Example

Solution

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.

Graph

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

The image is under
the reflection in the origin.