# Reflecting a Shape in y = −x Using Cartesian Coordinates(KS3, Year 7)

homesitemapgraphs and coordinatesreflecting shapes in the line y = −x
A shape can be reflected in the line y = −x. If point on a shape is reflected in the line y = −x:
The image below shows a point on a shape being reflected in the line 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.

## 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:

## Lesson Slides

The slider below shows another real example of how to reflect a shape in the line y = −x using Cartesian coordinates. Open the slider in a new tab

## 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.

This page was written by Stephen Clarke.

## You might also like...

#### Help Us Improve Mathematics Monster

• Do you disagree with something on this page?
• Did you spot a typo?
Please tell us using this form.

#### Find Us Quicker!

• When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.