A 270^(∘) rotation counterclockwise about the origin will change the coordinates of the vertices such that r_((270^(∘),O))(x,y)=(y,- x).
W'(-1,-3) X'(2,-5) Y'(8,0) Z'(-1, -2)
Practice makes perfect
Let's start by graphing the given coordinates so that we can see the polygon.
When a figure is rotated 270^(∘) counterclockwise about the origin, the coordinates of the image's vertices will change in the following way.
r_((270^(∘),O))(x,y)=(y,- x)
Using this rule and the vertices of the polygon, we can find the x- and y-coordinates of the image's vertices.
(x,y)
(y,- x)
W(3,-1)
W'(-1,-3)
X(5,2)
X'(2, - 5)
Y(0,8)
Y'(8,0)
Z(2,- 1)
Z'(-1,-2)
Knowing the vertices of r_((270^(∘),O))(WXYZ), we can draw the image.
