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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, 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:- The point A has Cartesian coordinates (2, 3).
- The reflected point A' has Cartesian coordinates (3, 2). The x-coordinate of A (2) has become the y-coordinate of A'. The y-coordinate of A (3) has become 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 | 1 | 6 |
B | 4 | 5 |
C | 1 | 4 |
2
Find the Cartesian coordinates of the reflected points.
Swap the x-coordinate and the y-coordinate of the original point.
Point | x-coordinate | y-coordinate | Point | x-coordinate | y-coordinate |
---|---|---|---|---|---|
A | 1 | 6 | A' | 6 | 1 |
B | 4 | 5 | B' | 5 | 4 |
C | 1 | 4 | C' | 4 | 1 |
3
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?