Question

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.

5
one fifth
12
one twelfth

Answer 1

To find the scale factor used in the dilation, we can compare the distance between corresponding pairs of vertices in the original triangle and the dilated triangle.

For example, we can compare the distance between A and B in the original triangle to the distance between A' and B' in the dilated triangle.

Distance between A and B:
sqrt[(3 - (-3))^2 + (3 - (-3))^2] = sqrt[72] = 6sqrt[2]

Distance between A' and B':
sqrt[(15 - (-15))^2 + (15 - (-15))^2] = sqrt[1800] = 30sqrt[2]

The scale factor is the ratio of the distance between corresponding pairs of vertices in the dilated triangle to the distance between the same pairs of vertices in the original triangle.

So, the scale factor used in the dilation is:

(scale factor) = (distance between corresponding vertices in dilated triangle) / (distance between corresponding vertices in original triangle)
= (30sqrt[2]) / (6sqrt[2])
= 5

Therefore, the scale factor used in the dilation is 5.