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# 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.## 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 | 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.

## Answer:

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:

## 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**

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