Reflection in the Origin Matrix

Reflection in the Origin Matrix

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

Matrix

The reflection in the origin matrix is [-1 0 / 0 -1], which is -I. To find the coordinates of the image, multiply the reflection matrix and the vertex matrix.

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

To find the coordinates of the image,
multiply the reflection matrix and the vertex matrix:
[-1 0 / 0 -1][x / y] = [-x + 0 / 0 - y] = [-x / -y].

Example

Triangle ABC has vertices A(1, 2), B(5, 4), and C(3, 1). Its image is under a reflection in the origin. Find the coordinates of the vertices of the image.

Previously, you've solved this example.

Reflection in the origin

Let's solve the same example
by using the reflection matrix.

Multiply the reflection matrix and the vertex matrix:
[-1 0 / 0 -1][1 5 3 / 2 4 1] = [-1 -5 -3 / -2 -4 -1].

Then the vertices of the image are
A'(-1, -2), B'(-5, -4), C'(-3, -1).

You can see that
by multiplying the reflection matrix, [-1 0 / 0 -1],
you can find the vertices of the image,
which is under the reflection in the origin.