Determine the scale factor used in the dilation of line segment AB , with a center point of dilation at the origin.

Question

A(9,9) -> B(6,6)

A(3,3) -> B(2,2)

Answer 1

In this case, the scale factor is 3, which can be determined by comparing the coordinates of the original segment AB and the dilated segment.

Original segment AB: (9, 9) -> (6, 6)
Dilated segment AB: (3, 3) -> (2, 2)

To find the scale factor, we can divide the change in the x-coordinate by the change in the y-coordinate:

Change in x-coordinate: 9 - 6 = 3
Change in y-coordinate: 9 - 6 = 3

Scale factor = Change in x-coordinate / Change in y-coordinate
Scale factor = 3 / 3
Scale factor = 1

Therefore, the scale factor used in the dilation of line segment AB is 3.