Point B is the image of point A under a dilation with center O and scale factor 7. If AB=44 the what is OA?

Question

Thorough explanations would be amazing!!

Answer 1

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

Solve for OA. The answer is a mixed number.