A rotation is a transformation about a fixed point called center of rotation. Each point of the original figure and its image are the same distance from the center of rotation. When a counterclockwise rotation is performed about the origin, the coordinates of the image can be written in relation to the coordinates of the preimage.
We want to rotate a quadrilateral 90^(∘) counterclockwise about the origin. Therefore, we can use the coordinate changes shown in the above table to determine the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y, x) [0.5em]
A( 1,3) & & A'(- 3,1) [0.5em]
B(2,5) & & B'(- 5, 2) [0.5em]
C(3,5) & & C'(- 5,3) [0.5em]
D(2,3) & & D'(- 3,2)
We can now plot the obtained points and draw the image of the given quadrilateral after the rotation!
Extra
Visualizing the Rotation
Let's rotate ABCD 90^(∘) counterclockwise about the origin so that we can see how it is mapped onto A'B'C'D'.
