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Math Help - Find the point on line...That is equidistant from...

  1. #1
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    Find the point on line...That is equidistant from...

    Hi My question is:

    Find the point on the line 4x-2y+3=0 that is equidistant from (3,3) and (7,-3)

    I'm still a little confused about what to do.

    Some ideas: I set 4x-2y+3=0 to y=2x + 3/2
    and that gives me the y-intercept


    Now, I was thinking that I need to find x with a distance formula.


    For example, find the distance formula for (3,3), then a second distance formula for (7,-3) and equal them to each other. Plugging in the y-intercept, then solving for x. I tried that, but I had an odd answer.

    If anybody could help me out that would be great! thanks
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by kn336a View Post
    Hi My question is:

    Find the point on the line 4x-2y+3=0 that is equidistant from (3,3) and (7,-3)

    I'm still a little confused about what to do.

    Some ideas: I set 4x-2y+3=0 to y=2x + 3/2
    and that gives me the y-intercept


    Now, I was thinking that I need to find x with a distance formula.


    For example, find the distance formula for (3,3), then a second distance formula for (7,-3) and equal them to each other. Plugging in the y-intercept, then solving for x. I tried that, but I had an odd answer.

    If anybody could help me out that would be great! thanks
    See your question is just a use of disance of a point from line

    the distance of a point
    (x_1,y_1) from line  ax+by+c=0 is given by

     <br />
|{\frac{ax_1+by_1+c} {\sqrt{a^2+b^2}}}|<br />
    Use it to find and equate those distances
    Last edited by ADARSH; February 8th 2009 at 09:47 PM. Reason: explanation added
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  3. #3
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    Quote Originally Posted by kn336a View Post
    Find the point on the line 4x-2y+3=0 that is equidistant from (3,3) and (7,-3)
    Find the equation of the perpendicular bisector of the line segment with endpoints (3,3) and (7,-3).
    Its slope must be \frac{2}{3} and contain the midpoint (5,0).
    Using that line find its intersection with the given line.
    That point is the answer to this question.
    Last edited by Plato; February 9th 2009 at 03:53 AM.
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