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

## The Lesson

A shape can be reflected in the x-axis. If point on a shape is reflected in the x-axis, the x-coordinate stays the same, but the y-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 x-axis: • The point A has Cartesian coordinates (3, 1).
• The reflected point A' has Cartesian coordinates (3, −1). The x-coordinate is still 3, but the y-coordinate has changed from 1 to −1.

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

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

## Question

Reflect the shape below in the x-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 2 3
B 5 2
C 2 1

# 2

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

# 3

Plot the reflected points and draw in the shape.

We have reflected the shape in the x-axis. ## A Formula to Reflect a Point in the X-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 x-axis: ## Lesson Slides

The slider below shows another real example of how to reflect a shape in the x-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.
Help Us To Improve Mathematics Monster