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:

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.
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See Also

What is geometry? What are transformations? What is the x-axis? What are Cartesian coordinates? What is the x-coordinate? What is the y-coordinate?