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

Answer 1

this is what came with the question in my exam , but i dont

know the answer and i couldn't comment the picture so can someone help?

Answer 2

A) U′ (0, 1), V′ (2, 2), W′ (2, 0)

Explanation:

The coordinate plane showing Triangle UVW is found online and attached below.

From the graph, the coordinates of the vertices of the triangle are:

U(0,3), V(6,6) and W(6,0)

When you dilate a point (x,y) with a scale factor of 1/3, you obtain:
`\left((x)/(3), (y)/(3)\right)`

Therefore, applying the dilation
`(x,y) \rightarrow \left((x)/(3), (y)/(3)\right)`, we have:

`U(0,3) \rightarrow U'((0)/(3) ,(3)/(3))=U'(0 ,1)\\\\V(6,6) \rightarrow V'((6)/(3) ,(6)/(3))=V'(2 ,2)\\\\W(6,0) \rightarrow W'((6)/(3) ,(0)/(3))=W'(2 ,0)`

The coordinates of the resulting triangle U′V′W′ are:

U′ (0, 1), V′ (2, 2), W′ (2, 0)

The correct option is A.