Reflection: y = x

How to find the image under the reflection in y = x: formula, 2 examples, and their solutions.

Formula

Formula

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

Switch x and y.

Example 1

Example

Solution

The image of (5, 2) is
under the reflection in y = x.

Then the image point is,
switch x and y,
(2, 5).

So (2, 5) is the answer.

Graph

This is the graph of (5, 2)
and its image
under the reflection in y = x:
(2, 5).

Example 2

Example

Solution

The image of [y = x2] is
under the reflection in y = x.

Then the image function is,
switch x and y,
x = y2.

So [x = y2] is the answer.

Parabola: Formula

You can change this in [y = ...] form:
y = ±√x.

Square Root Function: Graph

Graph

This is the graph of [y = x2]
and its image
under the reflection in y = x:
x = y2.