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:

enter image description here

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: $$ {5-m\over5+m}=0.6 \quad\hbox{and}\quad m={5\over4}. $$

  • $\begingroup$ Incorrect, because 0.6 is the hometecia $\endgroup$ – Eduardo Sebastian Sep 26 '17 at 22:08
  • $\begingroup$ Incorrect? What is your definition of homothety? With the usual definition, $P$ is the image of $S$, and $O$ is the center, so $PO/SO=0.6$. $\endgroup$ – Aretino Sep 27 '17 at 15:23
  • $\begingroup$ right, you recently edited the answer, thanks Aretino, That was my answer before I asked here, but how can I prove it? Why if you realize, more than one alternative is correcti do (5+m) + (5-m)*0.6 = 10 $\endgroup$ – Eduardo Sebastian Sep 27 '17 at 16:18
  • $\begingroup$ There is nothing to prove: it is the definition of homothety, which once again I urge you to look up. And I don't see any other correct alternatives. $\endgroup$ – Aretino Sep 27 '17 at 16:21
  • $\begingroup$ Oh thanks aretino, sorry for my bad knowledge :( $\endgroup$ – Eduardo Sebastian Sep 27 '17 at 16:26

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