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

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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:

reflect a shape in x-axis_cartesian_coordinates

reflect a shape in x-axis_cartesian_coordinates

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. reflect a shape in x-axis_cartesian_coordinates_example

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.

reflect a shape in x-axis_cartesian_coordinates_answer

A Formula to Reflect a Point in the X-Axis Using Cartesian Coordinates

In general, we write Cartesian coordinates as: cartesian_coordinate_point

x is the x-coordinate. y is the y-coordinate. x and y can taken any number. The reflected point has Cartesian coordinates:

cartesian coordinate point reflected in x-axis