26-06-2012, 16:37 #1 fade out Registered User   Join Date: May 2009 Posts: 23 Dividing a line in given ratio (brain freeze) Can someone help I can't figure out where I have gone wrong here. It is probably staring at me in the face but I have got brain freeze or something! A(4,-3) and B(-2,0) are the end points of a line segment. The point P(2,-2) divides [AB] internally in the ratio h:k. Find h:k. I have subbed in the co ordinates into the formula for internal division and then let each coordinate equal to a coordinate in P(2,-2). The equations I get from this however are no good as I seem to end up with -4h+2k=0 and 2h-k=0. Can someone point where I have gone wrong?
 26-06-2012, 16:43 #2 im invisible Closed Account   Join Date: Feb 2011 Posts: 4,188 just take either the x or the y values, Y makes it easier A -3 P -2 B 0 so thats 1:2
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 26-06-2012, 16:52 #3 Delphi91 Registered User     Join Date: May 2001 Location: Limerick Posts: 1,315 You could always use the "length of a line" formula to calculate |AP| and |PB|. Let H = |AP| and K=|PB|. Put them together in a ratio and simplify.
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 26-06-2012, 16:52 #4 fade out Registered User   Join Date: May 2009 Posts: 23 Thanks invisible! Is there a method using the formula though? Also your method works too Delphi thank you! Last edited by fade out; 26-06-2012 at 17:01.
 27-06-2012, 00:12 #5 MathsManiac Moderator     Join Date: Apr 2007 Posts: 1,327 Mod: Mathematics You didn't go wrong. Either one of your two equations tells you that k=2h, so that tells you that h:k is 1:2, or 2:4, or 3:6, etc., which all represent the same ratio, as long as the second number is twice the first. (The fact that your two equations are equivalent just confirms that the given point is indeed on the line AB)