# 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 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.

## 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.

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.

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