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), a

Question

elixir [45]

2 years ago

7

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), a

nd C′(15, 0). The origin is the center of dilation. What is the scale factor of the dilation?

Mathematics

1 answer:

Vesnalui [34] · Answer 1 · 2022-03-29T19:54:58+03:00

Answer:

2.5

Step-by-step 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

$\dfrac{A'B'}{AB}=\dfrac{A'C'}{AC}.$

Since

AB=4;
A'B'=10;
AC=6;
A'C'=15,

then the scale factor of the dilation is

$k=\dfrac{10}{4}=\dfrac{15}{6}=2.5.$