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)((0)/(3),(3)/(3))\text{ = U'(0, 1)} \\ V^(\prime)((6)/(3),\text{ }(6)/(3))\text{ = V'(2, 2)} \\ W^(\prime)((6)/(3),\text{ }(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