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?

Rationale

(2,4), (6,6), (10,16)

The triangle with vertices (2,4), (6,6), and (10,16) is an enlarged similar triangle with a scale factor of 2, as each vertex of the original triangle is multiplied by 2. This transformation preserves the shape of the triangle while increasing its size proportionally.

A ((1,1), (3,2), (5,4)) YOUR ANSWER

This triangle does not maintain the proportions of the original triangle because the vertices do not correspond to a doubling of the original coordinates. The resulting shape is not similar to the original triangle.

B ((1,4), (3,6), (5,10)) YOUR ANSWER

While this triangle has some vertices that appear to be scaled, the proportions do not align with those of the original triangle. The ratios of the sides are not consistent with those of the original triangle, thus failing to be similar.

D ((3,4), (5,6), (7,10)) YOUR ANSWER

This set of vertices resembles a different triangle that is neither enlarged nor similar to the original triangle. The side lengths do not maintain the same ratios as those in the original triangle, indicating a lack of similarity.

Conclusion

For a triangle to be similar and scaled by a factor, each vertex must be exactly double the corresponding vertex of the original triangle. The only choice that meets this criterion is (2,4), (6,6), and (10,16), confirming that it is an enlarged version of the original triangle with a scale factor of 2. The other options do not maintain the necessary proportions, resulting in triangles that are not similar.

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?

(2,4), (6,6), (10,16)

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