Question

the two figures are similar

Answer 1

Answer:

Part a) $\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}$

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure.(the scale factor is greater than 1)

Part c) The scale factor is $3$

Step-by-step explanation:

Part a) Write the similarity statement

we know that

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

so

$\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}$

substitute the values

$\frac{9}{27}=\frac{12}{36} =\frac{15}{45}$

$\frac{1}{3}=\frac{1}{3} =\frac{1}{3}$ ----> is true

therefore

the figures are similar

Part b) The dilation is an enlargement, because the sides of the image are larger than the sides of the original figure. (the scale factor is greater than 1)

Part c) we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z------> the scale factor

x-----> corresponding side of the image

y------> corresponding side of the original figure

so

$z=\frac{x}{y}$

we have

$x=A'B'=27\ units$

$y=AB=9\ units$

substitute

$z=\frac{27}{9}=3$

The scale factor is greater than 1

therefore

Is an enlargement