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?

Answer 1

the scale factor is definently 3

Explanation:

Answer 2

Scale factor is 3.

Explanation:

Given: The Line Segment AB is dilated and a line segment A'B' is created.

A' (0, 6) and B' (6, 9).

As per the given graph , we can easily see that the coordinates of A and B are

A(0, 2) and B(2, 3)

Please refer to attached graph for the coordinates of A', B' and A, B.

The distance formula is given as:

`D =√((x_2-x_1)^2+(y_2-y_1)^2)`

D is the distance between two coordinates
`(x_1,y_1)` and
`(x_2,y_2)`.

So, the distance AB =
`√((2-0)^2+(3-2)^2) = √(5)`

Similary, distance A'B' =
`√((6-0)^2+(9-6)^2) = √(36 + 9)=√(45) = 3√(5)`

We can clearly see that A'B' is three times the distance AB.

So, The scale factor 3.