Question

Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?
A. 1/2


B. 2


C. 3


D. 4

Answer 1

Answer:

The answer is "Option C"

Step-by-step explanation:

Given:

point A' and B'  are:  (0, 6)  (6, 9)

To above points we calculate point AB that is (0,2) and (2,3)

Distance formula:

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

calcuate AB point distance:

$x_1=0\\y_1=2\\x_2=2\\y_2=3$

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

    $=\sqrt{2^2+1^2}\\\\=\sqrt{4+1}\\\\=\sqrt{5}$

calculating A'B' point distance:

$x_1=0\\y_1=6\\x_2=6\\y_2=9$

$D=\sqrt{(6-0)^2+(9-6)^2}$

   $= \sqrt{(6)^2+(3)^2}\\\\= \sqrt{36+9}\\\\= \sqrt{45}\\\\= \sqrt{3\times 3\times 5}\\\\= 3\sqrt{5}$

If we divide:

$=\frac{3\sqrt{5}}{\sqrt{5}}\\\\=3$

The final answer is "3".