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September 16th, 2012, 06:51 PM  #1 
Joined: Sep 2012 Posts: 15 Thanks: 0  Find the point on the line that is equidistant from 2 points
Find the point (x, y) on the line y=1 x + 2 that is equidistant from the points (?2, 2) and (?10, 4). I missed my last lecture and she explained to the class about these types of equations! I don't have a buddy in the math class yet so I couldn't turn to anyone for help! Could someone please answer this practice question so I can look at the steps and understand it? Would be greatly appreciated! Thank you! 
September 16th, 2012, 06:56 PM  #2 
Global Moderator Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,131 Thanks: 428 Math Focus: Calculus/ODEs  Re: Find the point on the line that is equidistant from 2 po
Is your line ?

September 16th, 2012, 07:17 PM  #3 
Joined: Sep 2012 Posts: 15 Thanks: 0  Re: Find the point on the line that is equidistant from 2 po
I think the question is messed up or something.... I have the points distance and midpoint, but when I plug it into that line it makes the question incorrect..... Distance: sqrt68 Mid point: (6,4) 
September 16th, 2012, 07:34 PM  #4 
Global Moderator Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,131 Thanks: 428 Math Focus: Calculus/ODEs  Re: Find the point on the line that is equidistant from 2 po
I'll show you the general method by deriving a formula for any nonvertical line and two arbitrary points. Let the line be and the two arbitrary point be We let the point on the line be and we equate the square of the distances from this point on the line to the two arbitrary points: Next, we expand the squared binomials: Remove terms common to both sides: Arrange with terms involving x on the left and the rest on the right: Factor 2x from the left side: Divide through by 
September 17th, 2012, 02:00 PM  #5  
Senior Member Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Find the point on the line that is equidistant from 2 po Quote:
 
September 17th, 2012, 03:35 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 12,148 Thanks: 478 
The midpoint of the line segment joining (2, 2) and (10, 4) is (6, 3). The line y = 4x + 27 is the perpendicular bisector of that line segment, so every point on that line is equidistant from the points (2, 2) and (10, 4). Find where that line intersects the line given in the question.

September 18th, 2012, 06:35 PM  #7  
Joined: Sep 2012 Posts: 15 Thanks: 0  Re: Quote:
All of you! Thank you so much for the help!!!  

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