**y = x**. If point on a shape is reflected in the line

**y = x**, the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate. The image below shows a point on a shape being reflected in the line

**y = x**:

- The point
**A**has Cartesian coordinates**(2, 3)**. - The reflected point
**A'**has Cartesian coordinates**(3, 2)**. The x-coordinate of**A**(2) has become the y-coordinate of**A'**. The y-coordinate of**A**(3) has become the x-coordinate of**A'**.

## How to Reflect a Shape in *y = x* Using Cartesian Coordinates

Reflecting a shape in the line **y = x**using Cartesian coordinates is easy.

## Question

Reflect the shape below in the line**y = x**.

## Step-by-Step:

## 1

Find the Cartesian coordinates of each point on the shape.
Write the x-coordinates and y-coordinates of each point.

Point | x-coordinate | y-coordinate |
---|---|---|

A | 1 | 6 |

B | 4 | 5 |

C | 1 | 4 |

## 2

Find the Cartesian coordinates of the reflected points.
Swap the x-coordinate and the y-coordinate of the original point.

Point | x-coordinate | y-coordinate | Point | x-coordinate | y-coordinate |
---|---|---|---|---|---|

A | 1 | 6 | A' | 6 | 1 |

B | 4 | 5 | B' | 5 | 4 |

C | 1 | 4 | C' | 4 | 1 |

## 3

Plot the reflected points and draw in the shape.

## Answer:

We have reflected the shape in the line y = x.## A Formula to Reflect a Point in *y = x* Using Cartesian Coordinates

In general, we write Cartesian coordinates as:
**x**is the x-coordinate.

**y**is the y-coordinate.

**x**and

**y**can taken any number. The reflected point has Cartesian coordinates:

The image below shows a general Cartesian coordinate being reflected in the line

**y = x**:

## What Is a Reflection?

A reflection flips a shape so that it becomes a mirror image of itself. A reflection is a type of transformation.## You might also like...

graphs and coordinate geometryreflecting shapes in the y-axisreflecting shapes in the line y = −xunderstanding the basic equation of a circle

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