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

**y = −x**:

- both coordinates change sign (the coordinate becomes negative if it is positive and vice versa)
- the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate

**y = −x**:

- The point
**A**has Cartesian coordinates**(−3, 5)**. - The reflected point
**A'**has Cartesian coordinates**(−5, 3)**. The x-coordinate of**A**(−3) has its sign changed (3) and becomes the y-coordinate of**A'**. The y-coordinate of**A**(5) has its sign changed (−5) and becomes 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 | −6 | 3 |

B | −3 | 2 |

C | −6 | 1 |

## 2

Change the sign of both coordinates.
Make them negative if they are positive and positive if they are negative.

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

A | −6 | 3 | 6 | −3 |

B | −3 | 2 | 3 | −2 |

C | −6 | 1 | 6 | −1 |

## 3

Using the new coordinates from

**Step 2**(that have had their signs changed), make the x-coordinate the y-coordinate and the y-coordinate the x-coordinate.−x-coordinate | −y-coordinate | Point | x-coordinate | y-coordinate |
---|---|---|---|---|

6 | −3 | A' | −3 | 6 |

3 | −2 | B' | −2 | 3 |

6 | −1 | C' | −1 | 6 |

## 4

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 line y = xunderstanding the basic equation of a circleunderstanding the equation of a circle

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