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Math Help - The shortest distance from Point A to the line...

  1. #1
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    The shortest distance from Point A to the line...

    I really need some help with finding out the Shortest distance from
    Point A (2,0) to the line X-Y+4=0.
    It would be nice if someone could
    explain the steps to answering this question.
    (You can leave out the actual distance formula since I'm well aware of how that works)
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  2. #2
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    Quote Originally Posted by DPXJube View Post
    I really need some help with finding out the Shortest distance from
    Point A (2,0) to the line X-Y+4=0.
    It would be nice if someone could
    explain the steps to answering this question.
    (You can leave out the actual distance formula since I'm well aware of how that works)
    Find a normal vector from the line running through the point.
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  3. #3
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    dwsmith is exactly right. The shortest distance to a geometric object is always along the line perpendicular to that object.

    Here, the line is x- y+ 4= 0 which is the same as y= x+ 4. What is the slope of that line?

    What is the slope of a line perpendicular to that line? What is the equation of a line with this new slope and passing through (2, 0)?

    Where do those two lines intersect?

    What is the distance from the point of intersection to (2, 0)?
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