▸▸▸

Reflecting a Shape in y = −x Using Cartesian Coordinates

(KS3, Year 7)

A shape can be reflected in the line y = −x. If point on a shape is reflected in the line y = −x:

both coordinates change sign (the coordinate becomes negative if it is positive and vice versa)
the x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate

The image below shows a point on a shape being reflected in the line y = −x:

reflect a shape in y=-x_cartesian_coordinates

The point A has Cartesian coordinates (−3, 5).
The reflected point A' has Cartesian coordinates (−5, 3). The x-coordinate of A (−3) has its sign changed (3) and becomes the y-coordinate of A'. The y-coordinate of A (5) has its sign changed (−5) and becomes the x-coordinate of A'.

How to Reflect a Shape in y = −x Using Cartesian Coordinates

Reflecting a shape in the line y = −x using Cartesian coordinates is easy.

Question

Reflect the shape below in the line y = −x. reflect a shape in y=-x_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	−6	3
B	−3	2
C	−6	1

2

Change the sign of both coordinates. Make them negative if they are positive and positive if they are negative.

Point	x-coordinate	y-coordinate	−x-coordinate	−y-coordinate
A	−6	3	6	−3
B	−3	2	3	−2
C	−6	1	6	−1

3

Using the new coordinates from Step 2 (that have had their signs changed), make the x-coordinate the y-coordinate and the y-coordinate the x-coordinate.

−x-coordinate	−y-coordinate	Point	x-coordinate	y-coordinate
6	−3	A'	−3	6
3	−2	B'	−2	3
6	−1	C'	−1	6

4

Plot the reflected points and draw in the shape.

Answer:

We have reflected the shape in the line y = −x.

reflect a shape in y=-x_cartesian_coordinates_answer

A Formula to Reflect a Point in y = −x 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 y=-x