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September 16th, 2012, 06:51 PM   #1
 
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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!
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September 16th, 2012, 06:56 PM   #2
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Re: Find the point on the line that is equidistant from 2 po

Is your line ?
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September 16th, 2012, 07:17 PM   #3
 
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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)
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September 16th, 2012, 07:34 PM   #4
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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 non-vertical 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



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September 17th, 2012, 02:00 PM   #5
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Re: Find the point on the line that is equidistant from 2 po

Quote:
Originally Posted by elifast
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)
You are assuming that the two points are on the given line and that is not true.
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September 17th, 2012, 03:35 PM   #6
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The mid-point 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.
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September 18th, 2012, 06:35 PM   #7
 
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Re:

Quote:
Originally Posted by skipjack
The mid-point 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.
Thank you so much! You're honestly a life saver!

All of you!
Thank you so much for the help!!!
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