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

The answer is "Option C"

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=√((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=√((2-0)^2+(3-2)^2)`

`=√(2^2+1^2)\\\\=√(4+1)\\\\=√(5)\\`

calculating A'B' point distance:

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

`D=√((6-0)^2+(9-6)^2)`

`= √((6)^2+(3)^2)\\\\= √(36+9)\\\\= √(45)\\\\= √(3* 3* 5)\\\\= 3√(5)\\\\`

If we divide:

`=(3√(5))/(√(5))\\\\=3`

The final answer is "3".