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′?Question options:A) U′ (0, 2), V′ (3, 3), W′ (4, 0)B) U′ (0, 9), V′ (18, 18), W′ (18, 0)C) U′ (0, 1), V′ (3, 3), W′ (2, 0)D) U′ (0, 1), V′ (2, 2), W′ (2, 0)

Answer 1

First, we should identify the coordinates of the vertices of the triangle UVW.

The coordinates of the vertices are:

U(0,3)

V(6,6)

W(6, 0)

We can find the coordinates of the resulting triangle after dilation, given that the center of dilation is the origin using the relationship:

$(x,\text{ y) }\rightarrow\text{ (kx, ky)}$

Where k is the scale factor

Applying this rule to the original coordinates of the triangle UVW, we have the new coordinates to be:

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

Hence, the coordinates of the resulting triangle are:

U'(0, 1)

V'(2,2)

W'(2,0)

Answer:

Option D