Question

Triangle ABC was dilated and translated to form similar triangle A'B'C'. On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6). What is the scale factor of the dilation?

Answer 1

Scale factor is 2.5.

Explanation:

The triangles are drawn below.

From the triangle ΔABC,

AB = 2 units, BC = 2 units

From the triangle ΔA'B'C',

A'B' = 5 units, B'C' = 5 units.

Scale factor of a dilated figure is given as:

Scale factor =
`\frac{\textrm{New length}}{\textrm{Old length}}=(A'B')/(AB)=(B'C')/(BC)=(5)/(2)=2.5`

Therefore, the scale factor is 2.5.