Reflecting a Shape in the Y-Axis Using Cartesian Coordinates
(KS3, Year 7)
The LessonA shape can be reflected in the y-axis. If point on a shape is reflected in the y-axis, the y-coordinate stays the same, but the x-coordinate changes sign (becomes negative if it is positive and vice versa). The image below shows a point on a shape being reflected in the y-axis:
- The point A has Cartesian coordinates (3, 4).
- The reflected point A' has Cartesian coordinates (−3, 4). The y-coordinate is still 4, but the x-coordinate has changed from 3 to −3.
How to Reflect a Shape in the Y-Axis Using Cartesian CoordinatesReflecting a shape in the y-axis using Cartesian coordinates is easy.
QuestionReflect the shape below in the y-axis.
Find the Cartesian coordinates of each point on the shape. Write the x-coordinates and y-coordinates of each point.
Find the Cartesian coordinates of the reflected points. Keep the y-coordinate the same, but change the sign of the x-coordinate.
Plot the reflected points and draw in the shape.
Answer:We have reflected the shape in the y-axis.
A Formula to Reflect a Point in the Y-Axis 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 y-axis:
Lesson SlidesThe slider below shows another real example of how to reflect a shape in the y-axis 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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