Question

line segment BO is dilated through point B. The resulting segment is BO'. If BO measured 27 inches and BO' measured 9 inches what scale factor took BO to BO'?

Answer 1

Scale factor is defined as
s=size of image / size of preimage.

Here BO is preimage.
B'O'=BO' is image, since the position of B is invariant, so B=B'.

So scale factor = B'O'/BO = 9/27 = 1/3.