Question:
Triangle CBD has been dilated.
A. Determine the scale factor of the sides (small to large).
B. What is the ratio of the areas (small to large)?
C. Write a generalization about the ratio of the sides and the ratio of the areas of similar figures.
es )

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

so

Let

z ----> the scale factor

The scale factor is equal to

substitute

simplify

Part B) What is the ratio of the areas (small to large)?

Area of the small triangle

Area of the large triangle

ratio of the areas (small to large)

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a