# Reflecting a Shape in the Y-Axis Using Cartesian Coordinates(KS3, Year 7)

homesitemapgraphs and coordinatesreflecting shapes in the y-axis
A shape can be reflected in the y-axis. If point on a shape is reflected in the y-axis, the y-coordinate stays the same, but the x-coordinate changes sign (becomes negative if it is positive and vice versa). The image below shows a point on a shape being reflected in the y-axis:

• The point A has Cartesian coordinates (3, 4).
• The reflected point A' has Cartesian coordinates (−3, 4). The y-coordinate is still 4, but the x-coordinate has changed from 3 to −3.

## How to Reflect a Shape in the Y-Axis Using Cartesian Coordinates

Reflecting a shape in the y-axis using Cartesian coordinates is easy.

## Question

Reflect the shape below in the y-axis.

## 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 −3 2
B −2 5
C −1 2

## 2

Find the Cartesian coordinates of the reflected points. Keep the y-coordinate the same, but change the sign of the x-coordinate.
Point x-coordinate y-coordinate Point x-coordinate y-coordinate
A −3 2 A' 3 2
B −2 5 B' 2 5
C −1 2 C' 1 2

## 3

Plot the reflected points and draw in the shape.

## Answer:

We have reflected the shape in the y-axis.

## A Formula to Reflect a Point in the Y-Axis 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 y-axis:

## Lesson Slides

The slider below shows another real example of how to reflect a shape in the y-axis 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.

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