Unit A: Geometry

Chapter 2: Transformations

Reflections in a Cartesian Plane


The process to reflect an object on a Cartesian plane uses the same method as reflecting in a vertical or horizontal line. Each point on a shape and the corresponding point on its image are the same distance from the line of reflection.

Reflect ABCD in the  x-axis. State the coordinates of each vertex for the isosceles trapezoid, ABCD, and its image, A'B'C'D'.
 






The line of reflection is the  x-axis.
The coordinates of quadrilateral ABCD are A(4, 5), B(5, 5), C(3, 3), D(6, 3).
The coordinates of image A'B'C'D' are A'(4, –5), B'(5, –5), C'(3, –3), D'(6, –3).
Reflect the following shape in the  y-axis.







The line of reflection is the y-axis.
The coordinates of quadrilateral ABCD are A(–3, 2), B(–1, 7), C(–6, 8), D(–8, 4).
The coordinates of image A'B'C'D' are A'(3, 2), B'(1, 7), C'(6, 8), D'(8, 4).

Watch the following video demonstrating the solution to Example 4. This video also includes a reflection in the x-axis.