Question

A triangle with vertices at A(0, 0), B(4, 0), and C(60, 15) is dilated to use a triangle with vertices at A'(0, 0), B'(Tenn), and C'(15, zero), with the origin as the center of dilation. What is the scale factor of the dilation?

Answer 1

The scale factor of the dilation is 0.

Step-by-step explanation:

To find the scale factor of the dilation, we can compare the corresponding sides of the original triangle and the dilated triangle.

The original triangle has side lengths AB = 4 units and BC = 61 units. The dilated triangle has corresponding side lengths A'B' = ? and B'C' = ?.

Using the formula for scale factor:

Scale Factor = Corresponding Length in Dilated Triangle / Corresponding Length in Original Triangle

Scale Factor = A'B' / AB = B'C' / BC

Scale Factor = A'B' / 4 = B'C' / 61

To find the missing side lengths in the dilated triangle, we can rearrange the equation:

A'B' = (Scale Factor) * AB = (Scale Factor) * 4

B'C' = (Scale Factor) * BC = (Scale Factor) * 61

Given that A'B' = 0 (since the vertex A remains fixed), we can substitute the values and solve for the scale factor:

0 = (Scale Factor) * 4

Scale Factor = 0 / 4 = 0

Therefore, the scale factor of the dilation is 0.