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 find the coordinates of the image of the quadrilateral after a 180^(∘) counterclockwise rotation 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) & → & (- x, - y) [0.5em]
S(- 4,- 2) & & S'(4,2) [0.5em]
T(- 2,- 2) & & T'(2, 2) [0.5em]
U(- 2,- 4) & & U'(2,4) [0.5em]
V(- 4, - 4) & & V'(4, 4)
Extra
Visualizing the Rotation
Let's rotate quadrilateral STUV 180^(∘) counterclockwise about the origin.
