# 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 = x^{2}] is

under the reflection in y = x.

Then the image function is,

switch x and y,

x = y^{2}.

So [x = y^{2}] 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 = x^{2}]

and its image

under the reflection in y = x:

x = y^{2}.