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Math Help - Finding point on a line closest to another line

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    Finding point on a line closest to another line

    Find the point on the line x + y − 2 = 0 that is closest to the point (-2, 5)
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  2. #2
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    Re: Finding point on a line closest to another line

    What you want is the intersection of the line perpendicular to the given line which passes through the given point. Can you proceed?
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    Re: Finding point on a line closest to another line

    So a line orthogonal to x + y - 2 = 0?
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    Re: Finding point on a line closest to another line

    Quote Originally Posted by biggerleaffan View Post
    So a line orthogonal to x + y - 2 = 0?
    Note that x-y+7=0 is a line through (-2,5) and perpendicular to the given line.

    Where do they intersect?
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    Re: Finding point on a line closest to another line

    Quote Originally Posted by Plato View Post
    Note that x-y+7=0 is a line through (-2,5) and perpendicular to the given line.

    Where do they intersect?
    -5/2, 9/2.

    Is this then the answer to my original question?
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    Re: Finding point on a line closest to another line

    Quote Originally Posted by biggerleaffan View Post
    -5/2, 9/2.
    Is this then the answer to my original question?
    I don't know if that is correct. I will not do the algebra.

    But by definition: the distance from a point to a line is the length of the line segment from the point to the line.
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    Re: Finding point on a line closest to another line

    Quote Originally Posted by Plato View Post
    I don't know if that is correct. I will not do the algebra.

    But by definition: the distance from a point to a line is the length of the line segment from the point to the line.
    There are many "line segments from the point to the line".

    By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line.
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    Re: Finding point on a line closest to another line

    Quote Originally Posted by HallsofIvy View Post
    There are many "line segments from the point to the line".

    By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line.
    RIGHT! I have no idea where my "perpendicular" went to. Clearly a typo. Thank you.
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