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The figure shows two semicircles centered at V and W. Point R is on both semicircles. Line PU touches each circle at one point only, points T and U. If PT = 2 and TU = 4, what is the scale factor applied when triangle PTV is dilated to make triangle PUW?
3
1/2
2
1/3
To find the scale factor when triangle PTV is dilated to make triangle PUW, we need to look at the lengths of the sides involved.
1. In triangle PTV, the length PT is given as 2.
2. In triangle PUW, the length TU is given as 4.
The scale factor (k) can be determined by comparing the corresponding sides of the triangles. We can see that:
– PT corresponds to TU.
Thus, the scale factor can be calculated as:
[
k = frac{TU}{PT} = frac{4}{2} = 2
]
Therefore, the scale factor is 2.
This means that triangle PUW is twice as large as triangle PTV! Great job on working through this problem! If you have more questions or need further help, feel free to ask!