# Proportional Segment

In the attached figure, a homotecia of ratio -0.6 and center O (0, m) transforms the horizontal segment FS, in segment PQ. If P and S are on the vertical axis, both to five units of the X-axis, then the value of m is:

I cant resolve this, in the guide the alternatives are:

a) 3/5
b) 3
c) 2
d) 5/3
e) 5/4


I understand that the PO segment would be (5 - m) And the segment FS would be (5 + m)

But i cant resolve that...

$${PO\over OS}=0.6,$$ hence: $${5-m\over5+m}=0.6 \quad\hbox{and}\quad m={5\over4}.$$
• Incorrect? What is your definition of homothety? With the usual definition, $P$ is the image of $S$, and $O$ is the center, so $PO/SO=0.6$. – Aretino Sep 27 '17 at 15:23