Question

Triangle ABC is dilated to form triangle A’B’C’. What is the dilation factor? What is the center of dilation? Select all that apply.

A.
dilation factor of 3

B.
dilation factor of 1/3
C.
center of dilation (−6,5)
D.
center of dilation (6,−5)

Answer 1

For the dilation factor find the scale of one of the sides:

AC is 11 units long

A'C' is 33 units long

33 / 11 = 3

The dilation factor is A. 3

Because both triangles are mostly to the left of the Y axis, the center of dilation would be located to the left, which would be a negative X value.

The center of dilation is C. (-6,5)

Answer 2

Answer:

A and C are the correct options.

Step-by-step explanation:

Triangle ABC is dilated to form triangle A'B'C'

We have to calculate the dilation factor.

As we know dilation factor is the ratio of sides in the previous image and image after dilation.

Dilation factor = $\frac{A'C'}{AC}$

                       = $\frac{12-(-21)}{0-(-11)}$

                       = $\frac{33}{11}$

                       = 3

Let the point of dilation is P(x, y)

Then distance PA and distance PA' will have a dilation factor of 3

$\frac{PA'}{PA}$ = 3

If the center of dilation is P(-6, 5) then ratio of distances from P to A and A' will represent dilation factor.

$\frac{PA'}{PA}=\frac{\sqrt{(-6+21)^{2}+(5-17)^{2}}}{\sqrt{(-6+11)^{2}+(5-9)^{2}}}$

$\frac{PA'}{PA}=\frac{\sqrt{(15)^{2}+(-12)^{2}}}{\sqrt{(5)^{2}+(-4)^{2}}}$

= $\frac{\sqrt{225+144}}{\sqrt{25+16}}$

= $\frac{\sqrt{369}}{\sqrt{41}}$  

= $\frac{19.20}{6.40}$

= 3

Therefore, center of dilation is (-6, 5).

A and C are the correct options.