Reflecting a Shape in y = −x Using Cartesian Coordinates
(KS3, Year 7)
The LessonA 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 CoordinatesReflecting a shape in the line y = −x using Cartesian coordinates is easy.
QuestionReflect the shape below in the line y = −x.
Find the Cartesian coordinates of each point on the shape. Write the x-coordinates and y-coordinates of each point.
Change the sign of both coordinates. Make them negative if they are positive and positive if they are negative.
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.
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 CoordinatesIn 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 SlidesThe slider below shows another real example of how to reflect a shape in the line y = −x using Cartesian coordinates. Open the slider in a new tab
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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