Question

After a dilation, triangle A (0,0), B(0,4), C (6,0) becomes triangle A’ (0,0), B’ (0, 10), C’ (15, 0). Choose the scale factor for this dilation.

A)
2

B)
2.5

C)
1.5

D)
3

Explain how you got the answer.

Answer 1

The scale factor for the dilation of triangle A(0,0), B(0,4), C(6,0) to triangle A'(0,0), B'(0,10), C'(15,0) is found by comparing the lengths of corresponding sides before and after dilation. The scale factor is calculated to be 2.5, which corresponds to option B.

Step-by-step explanation:

The student is asked to choose the scale factor for a dilation of a triangle. After dilation, the original coordinates of triangle A (0,0), B (0,4), C (6,0) become the coordinates for triangle A' (0,0), B' (0,10), C' (15,0). To find the scale factor, you can compare the lengths of corresponding sides before and after the dilation.

For point B, we look at the y-coordinate, which goes from 4 to 10. This means we have multiplied the original y-coordinate by 2.5 to get the new y-coordinate. So, the scale factor for point B is 2.5. Similarly, for point C, the x-coordinate goes from 6 to 15. Once again, we divide 15 by 6 to get 2.5. Therefore, the scale factor for point C is also 2.5. Since both points give the same scale factor, we conclude that the scale factor for the dilation of the whole triangle is indeed 2.5.

The correct answer is B) 2.5.