Exercise 2 Page 367

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.

Rotations About the Origin
90^(∘) Rotation	180^(∘) Rotation	270^(∘) Rotation
ccc Preimage & & Image [0.5em] (x,y) & → & (- y,x)	ccc Preimage & & Image [0.5em] (x,y) & → & (- x,- y)	ccc Preimage & & Image [0.5em] (x,y) & → & (y,- x)

We want to find the coordinates of the image of the quadrilateral after a 270^(∘) 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) & → & (y, - x) [0.5em] S(- 4,- 2) & & S'(- 2,4) [0.5em] T(- 2,- 2) & & T'(- 2, 2) [0.5em] U(- 2,- 4) & & U'(- 4,2) [0.5em] V(- 4, - 4) & & V'(- 4, 4)

Extra

Visualizing the Rotation

Let's rotate quadrilateral STUV 270^(∘) counterclockwise about the origin.