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((x)/(3),(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)=((0)/(3),(3)/(3))=(0,1) \\ V=(6,6)\longrightarrow V^(\prime)=((6)/(3),(6)/(3))=(2,2) \\ W=(6,0)\longrightarrow W^(\prime)=((6)/(3),(0)/(3))=(2,0) \end{gathered}`

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

The right option is Option D.