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^(∘) counterclockwise about the origin. A rotation by 270^(∘) counterclockwise ends up in the same place as a rotation by 90^(∘) clockwise. Therefore, we can use the coordinate changes shown in the table that correspond to a 90^(∘) clockwise to determine the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (y,- x) [0.5em]
W(- 6,-2) & & W'(- 2,6) [0.5em]
X(- 2,- 2) & & X'(- 2,2) [0.5em]
Y(- 2,- 6) & & Y'(-6,2) [0.5em]
Z(- 5,- 6) & & Z'(- 6,5)
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 WXYZ 270^(∘) counterclockwise about the origin so that we can see how it is mapped onto W'X'Y'Z'.
