Let's start by graphing the polygon with vertices W(-2,- 1), X(-1,3), Y(3,3), and Z(3,- 3).
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 graph the image of the given polygon after a 180^(∘) counterclockwise rotation about the origin. To do so, we can use the information in the above table to find the coordinates of the image of each vertex.
Point
(x,y)
(- x,- y)
W
(- 2,- 1)
(2,1)
X
(- 1,3)
(1,- 3)
Y
(3,3)
(- 3,- 3)
Z
(3,- 3)
(- 3,3)
Now that we know the vertices of the rotated figure, we can draw it.
