Question

Triangle UVW is dilated with a scale factor of 1/3 with the center of dilation at the origin. What are the coordinates of the resulting triangle U'V'W?

Answer 1

A dilation with a scale factor of k=1/3 with the center of dilation at the origin will perform the following transformation in any point (x,y):

$(x,y)\longrightarrow(\frac{x}{3},\frac{y}{3})$

We have a triangle with vertices U, V and W.

We apply the transformation to these points and get:

$\begin{gathered} U=(0,3)\longrightarrow U^{\prime}=(\frac{0}{3},\frac{3}{3})=(0,1) \\ V=(6,6)\longrightarrow V^{\prime}=(\frac{6}{3},\frac{6}{3})=(2,2) \\ W=(6,0)\longrightarrow W^{\prime}=(\frac{6}{3},\frac{0}{3})=(2,0) \end{gathered}$

Answer: U'=(0,1), V'=(2,2), W'=(2,0)

The right option is Option D.