Answer:
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
[tex]\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}[/tex]
The scale factor is equal to
[tex]z=\frac{CB}{C'B'}[/tex]
substitute
[tex]z=\frac{4}{8}[/tex]
simplify
[tex]z=\frac{1}{2}[/tex]
Part B) What is the ratio of the areas (small to large)?
Area of the small triangle
[tex]A=\frac{1}{2}(2)(4)=4\ units^2[/tex]
Area of the large triangle
[tex]A=\frac{1}{2}(4)(8)=16\ units^2[/tex]
ratio of the areas (small to large)
[tex]ratio=\frac{4}{16}=\frac{1}{4}[/tex]
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
