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October 31st, 2008, 07:06 PM  #1 
Newbie Joined: Oct 2008 Posts: 3 Thanks: 0  Length of a Line Segment
Hello everyone, I didn't know how to answer this question in my previous quiz. To be ready for the coming test, It would be great if anyone answers that question: The line segment WF has a length of squareroot 65 . If the endpoint W has the coordinates (9,3), I need to determine one possibility for the coordinates of the endpoint F. Please include in your solution detailed steps that lead to your final answer. It would help me alot if you provide either specific explanations or mathematical calculations or both to indicate how the information was obtained. 
October 31st, 2008, 08:32 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,716 Thanks: 1532 
By Pythagoras's theorem, the distance between (9, 3) and (2, 1) is the square root of (9  2)^2 + (3  (1))^2, i.e., the square root of 65.

November 1st, 2008, 09:23 AM  #3  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Length of a Line Segment Quote:
If the other point is (x,y), can you write an expression for the distance between (x,y) and (9,3)? You can then put that equal to the root of 65. Square both sides [the Pythagoras identity from which this all follows.] That will represent a circle which is a whole lot of points like the one you are looking for. Let y have some value [within certain limits which can be found with more analysis, but just give some reasonable guess for now, as skipjack did.] You can then find the corresponding xvalue.  
November 5th, 2008, 02:52 AM  #4 
Newbie Joined: Nov 2008 Posts: 2 Thanks: 0  Re: Length of a Line Segment
we can not find the other end point because it is not sufficient. or the point forms a locus. If we let the other point be (x,y) then we may a equation with distance formula (x9)^2+(y3)^2=65 which is actually the equation of a circle with center (9,3) and radius sq.root 65. And all the other end point are those which satisfy the above equation. And there are infinite solutions not specific one. Thanks 

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