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
The scale factor used is 5.
To find the scale factor, we can compare the distance between the corresponding vertices of the original and dilated triangle. For example, the distance between points A and B in the original triangle is 2√3, and in the dilated triangle it is 10√3.
Therefore, 10√3 / 2√3 = 5.
This means that each coordinate of the original triangle was multiplied by 5 to get the coordinates of the dilated triangle.