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 clockwise 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. A rotation by 90^(∘) counterclockwise ends up in the same place as a rotation by 270^(∘) clockwise. We can use the coordinate changes shown in the table that correspond to a 270^(∘) clockwise to determine the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y, x) [0.5em]
A( 2,-2) & & A'(2,2) [0.5em]
B(4,-1) & & B'(1, 4) [0.5em]
C(4,-3) & & C'(3,4) [0.5em]
D(2,- 4) & & D'(4,2)
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'.
