Reflection in the Line y = x Matrix

Reflection in the Line y = x Matrix

How to use the reflection in the line y = x matrix to find the image under the reflection: the matrix, example, and its solution.

Matrix

The reflection in the line y = x matrix is [0 1 / 1 0]. To find the coordinates of the image, multiply the reflection matrix and the vertex matrix.

The reflection in the line y = x matrix is
[0 1 / 1 0].

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

Example

Triangle ABC has vertices A(4, 1), B(7, 3), and C(5, -2). Its image is under a reflection in the line y = x. Find the coordinates of the vertices of the image.

Previously, you've solved this example.

Reflection in the line y = x

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

Multiply the reflection matrix and the vertex matrix:
[0 1 / 1 0][4 7 5 / 1 3 -2] = [1 3 -2 / 4 7 5].

Then the vertices of the image are
A'(1, 4), B'(3, 7), C'(-2, 5).

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