Question

3
triangle abc
is dilated to
create triangle
abc. what is
the ratio of the
area of triangle
abc to the area
of triangle abc?
a $\frac{1}{3}$
b $\frac{1}{9}$
c 3
d 9

Explanation:

Step1: Find side lengths of ABC

From the grid: $AB = 3$, $BC = 2$

Step2: Find side lengths of A'B'C'

From the grid: $A'B' = 9$, $B'C' = 6$

Step3: Find dilation scale factor

Scale factor $k = \frac{A'B'}{AB} = \frac{9}{3} = 3$

Step4: Find area ratio rule

Area ratio = $k^2$

Step5: Calculate area ratio

Area ratio = $3^2 = 9$

Answer:

D. $9$