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Reflecting a Shape in y = −x Using Cartesian Coordinates
(KS3, Year 7)
The Lesson
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 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.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.A Formula to Reflect a Point in y = −x 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 line y = −x:
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.- Do you disagree with something on this page?
- Did you spot a typo?