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 270^(∘) clockwise about the origin. Therefore, we can use the information in the above table to find the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y, x) [0.5em]
P(-3,4) & & P'(- 4,- 3) [0.5em]
Q(- 1,4) & & Q'(- 4,- 1) [0.5em]
R(- 2,1) & & R'(- 1,- 2) [0.5em]
S(- 4,1) & & S'(- 1,- 4)
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 PQRS 270^(∘) clockwise about the origin so that we can see how it is mapped onto P'Q'R'S'.
