5. A triangle has vertices (1,2), (3,4), and (5,8). Which of the following triangles with the indicated vertices would create an enlarged similar triangle with a scale factor of 2?
Answer: C
Triangle C creates an enlarged similar triangle with a scale factor of 2.
The triangle with vertices (2,4), (6,6), and (10,16) is an enlarged version of the original triangle with vertices (1,2), (3,4), and (5,8) with a scale factor of 2.
A) (1,1), (3,2), (5,4)
This triangle does not maintain similarity to the original triangle as the vertices do not correspond to a uniform scale factor from the original triangle. The distances and angles between the vertices do not match the proportionality required for similarity.
B) (1,4), (3,6), (5,10)
Although this triangle has some proportionality, it does not maintain the correct scale factor of 2 from the original triangle. The ratios of the sides do not correspond to the necessary enlargement.
C) (2,4), (6,6), (10,16)
This triangle is derived by multiplying each vertex of the original triangle by the scale factor of 2. Each vertex corresponds to the original triangle's vertices, confirming that the triangles are similar and enlarged by the correct factor.
D) (3,4), (5,6), (7,10)
This triangle fails to maintain the necessary properties of similarity to the original triangle. The vertices do not reflect a consistent scale factor, resulting in a triangle that is neither similar nor correctly enlarged.
Conclusion
Triangle C is the only option that accurately represents an enlarged similar triangle with a scale factor of 2. The other options either fail to maintain the necessary proportionality or do not correspond to the defined scale factor, thus confirming that option C is definitively the correct choice.