Question

A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B prime, has the coordinates (2, –3). What is the scale factor of the dilation? StartFraction 1 Over 10 EndFraction One-fifth 5 10

Answer 1

Answer:   1/5

Step-by-step explanation:

Answer 2

Answer:

One-fifth

Step-by-step explanation:

step 1

Find the distance between the origin and the point B

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

O (0,0) and B(10, –15)

substitute

$d=\sqrt{(-15-0)^{2}+(10-0)^{2}}$

$d=\sqrt{325}\ units$

step 2

Find the distance between the origin and the point B'

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

O (0,0) and B'(2,-3)

substitute

$d=\sqrt{(-3-0)^{2}+(2-0)^{2}}$

$d=\sqrt{13}\ units$

step 3

Find the scale factor of the dilation

The scale factor is equal to divide the length of segment OB' by the length of segment OB

so

$\frac{\sqrt{13}}{\sqrt{325}}=\frac{1}{5}$

so

One-fifth