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 image below shows a point on a shape being reflected in the line
y = −x:
-
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.
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:
Lesson Slides
The slider below shows another real example of how to reflect a shape in the line y = −x using Cartesian coordinates.
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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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