Question

A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A′(0, 0), B′(0, 10), and C′(15, 0). The origin is the center of dilation. What is the scale factor of the dilation?

Answer 1

2.5

Explanation:

A triangle ABC with vertices A(0, 0), B(0, 4), and C(6, 0) is dilated to form a triangle A'B'C' with vertices A′(0, 0), B′(0, 10), and C′(15, 0). If the center of dilation is point A or A' (the origin), then

`(A'B')/(AB)=(A'C')/(AC).`

Since

• AB=4;
• A'B'=10;
• AC=6;
• A'C'=15,

then the scale factor of the dilation is

`k=(10)/(4)=(15)/(6)=2.5.`