Question

Triangle ABC was dilated by 50%. What is the relationship between AC and A'C'?

Answer 1

Answer:

D)  1 /2 (AC) = A'C'

Step-by-step explanation:

The solution is  1 /2  AC = A'C'. The side lengths in ΔABC are twice the side lengths in ΔA'B'C'.

Answer 2

Answer:      

The length of segment AC is two times the length of segment A'C'

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ----> the scale factor

A'C' ----> the length of segment A'C'

AC ----> the length of segment AC

so

$z=\frac{A'C'}{AC}$                        

we have that

$z=50\%=50/100=\frac{1}{2}$ ---> the dilation is a reduction, because the scale factor is less than 1 and greater than zero

substitute

$\frac{1}{2}=\frac{A'C'}{AC}$                

$AC=2A'C'$

therefore

The length of segment AC is two times the length of segment A'C'