1. Point B is the image of point A under a dilation with center O and scale factor 7. If AB = 44, then what is OA?
O---------A----------------------------------------------------------------B
<--------------------------- 44 ------------------------------->
For a scale factor of 7, we have OB = 7·OA; that is, OB is 7 times longer than OA. The Segment Addition Postulate tells us that OB = OA + AB, so:
OB = 7·OA
OA + AB = 7·OA
Since AB = 44:
OA + 44 = 7·OA
OA = 7.3333
( I found this answer on the web)