Start by considering the preimage WXYZ and image W'X'Y'Z'.
First Transformation: Rotation of 90^(∘) about the origin Second Transformation: Translation along ⟨ 9,1 ⟩
Practice makes perfect
In this exercise, two transformations have been performed to map the figures. We will start by describing the transformation from the preimage WXYZ to the image W'X'Y'Z'.
Transformation from WXYZ to W'X'Y'Z'
We can see in the given graph that W'X'Y'Z' is a rotation of 90^(∘) about the origin of WXYZ.
When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the vertices will change in the following way.
(x,y)→ (- y,x)
Therefore, the transformation used to map W'X'Y'Z' is a rotation of 90^(∘) about the origin.
Transformation from W'X'Y'Z' to W''X''Y''Z''
We can see in the given graph that W''X''Y''Z'' is a translation right 9 unit, and up 1 of W'X'Y'Z'.
Vertical translations affect the y-coordinate and horizontal translations affect the x-coordinate. We can use this to write the translation from W'X'Y'Z' to the image W''X''Y''Z''.
(x,y)→(x + 9,y + 1)
Therefore, the transformation used to map W''X''Y''Z'' is a translation along vector ⟨ 9, 1 ⟩.
