Reflection in the Line y = x

Reflection in the Line y = x

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

Formula

The image of a point (x, y) under the reflection in the line y = x is (y, x).

The image of a point (x, y)
under the reflection in the line y = x is
(y, x).

To find the image,
switch x and y.

Example

Graph the given triangle and its image under the reflection in the line y = x on the coordinate plane. Triangle ABC with vertices A(6, 4), B(7, 1), and C(2, -2)

To find the image
under the reflection in the line y = x,
switch x and y.

The image of A(6, 4) is
A'(4, 6).

The image of B(7, 1) is,
switch x and y,
B'(1, 7).

The image of C(2, -2) is,
switch x and y,
C'(-2, 2).

ABC has vertices
A(6, 4), B(7, 1), and C(2, -2).

A'B'C' has vertices
A'(4, 6), B'(1, 7), and C'(-2, 2).

Use these vertices
to draw △ABC and its image △A'B'C'
on the coordinate plane.

As you can see,
A'B'C' is under the reflection in the line y = x.

The triangle is only filped.
There's no change in its size.

So, under a reflection,
not only in the line y = x,
the length and the area are reserved.