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Math Help - Straight line points

  1. #1
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    Straight line points

    Hi

    How to calculate straight line starting point x,y values(a) and ending point x,y values(b). I know the slope of the line , width of the line and center point of the line(c).

    Thanks in advance.
    Attached Thumbnails Attached Thumbnails Straight line points-line.png  
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  2. #2
    Super Member
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    Quote Originally Posted by kumar View Post
    Hi

    How to calculate straight line starting point x,y values(a) and ending point x,y values(b). I know the slope of the line , width of the line and center point of the line(c).

    Thanks in advance.
    If you know the slope, and a point on the line then
    what are you asking?

    I'm guessing here:
    Are you looking for the coordinates of a point that is
    equidistant left & right from the center point?


    X_a = X_c + HorizontalDistanceLeft

    Y_a = Y_c + HorizontalDistanceLeft \cdot Slope


    X_b = X_c + HorizontalDistanceRight

    Y_b = Y_c + HorizontalDistanceRight \cdot Slope


    You must be aware that
    the HorizontalDistanceLeft will be NEGATIVE &
    the HorizontalDistanceRight will be POSITIVE.
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  3. #3
    MHF Contributor

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    What do you mean by "calculate straight line"? If you know any one point on the line, a, or b, or c, and the slope, m, then the equation of the straight line is y= m(x- a_x)+ a_y= m(x- b_x)+ b_y= m(x- c_x)+c_y. You don't need to know the other points or the other information. If you know two points, say a and b, then you can calculate the slope, m= \frac{a_y- b_y}{a_x- b_x}.

    Do you mean "find the length of the line segment"? If so, any two of the facts you have will suffice.

    If you know the end points, a and b, the length is \sqrt{(a_x- b_x)^2+ (a_y- b_y)^2}.

    If you know and endpoint, either a or b, and the center point, c, then the length is 2\sqrt{a_x- c_x)^2+ (a_y- c_y)^2}.

    If you know the "width of the line" (by which, I take it, you mean the absolute value of the difference in x values of a and b) and the slope then, taking w= "width" and m= "slope", the "height", the absolute value of the difference in y value of a and b, is given by wm and so the length of the line segment is given by \sqrt{w^2+ (wm)^2}= w\sqrt{1+ m^2}.
    Last edited by HallsofIvy; September 1st 2009 at 05:22 PM.
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