Question

Rectangle ABCD with coordinates A(1,1), B(4,1), C(4,2) and D(1,2) dilates with respect to the origin to give rectangle A’B’C’D’. If A’B’=6 what is the scale factor of the dilation?
A: 6
B: 3
C: 2
D: 1/2
E: 4

Answer 1

Answer: Option C.

Step-by-step explanation:

You need to find the distance AB with the formula for calculate the distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:

$AB=\sqrt{(4-1)^2+(1-1)^2}=3$

You know that A'B'=6, then the scale factor of dilation can be calculated with:

$k=\frac{A'B'}{AB}$

Substituting values, you get:

$k=\frac{6}{3}\\\\k=2$

This matches with the option C.

Answer 2

C should be the answer