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September 16th, 2012, 07:51 PM | #1 |
Newbie 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! |
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September 16th, 2012, 07:56 PM | #2 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: Find the point on the line that is equidistant from 2 po
Is your line |
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September 16th, 2012, 08:17 PM | #3 |
Newbie 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) |
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September 16th, 2012, 08:34 PM | #4 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 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 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 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, 03:00 PM | #5 | |
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6 | Re: Find the point on the line that is equidistant from 2 po Quote:
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September 17th, 2012, 04:35 PM | #6 |
Global Moderator Joined: Dec 2006 Posts: 20,288 Thanks: 1968 |
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, 07:35 PM | #7 | |
Newbie Joined: Sep 2012 Posts: 15 Thanks: 0 | Re: Quote:
All of you! Thank you so much for the help!!! ![]() | |
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equidistant, find, line, point, points |
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