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Math Help - Straight Line Geometry Q

  1. #1
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    Straight Line Geometry Q

    The straight line L passes through the points A(6,4) and B(2,10)

    1) Find an equation of L expressing your answer in the form ax+by+c=0

    The point (-2,k) lies on the line L

    2) Find the value of k

    The line M has an equation y-x+12=0. Lines M and L intersect at point P.

    3) Find the coordinates of point P.
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  2. #2
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    Quote Originally Posted by x-disturbed-x
    The straight line L passes through the points A(6,4) and B(2,10)

    1) Find an equation of L expressing your answer in the form ax+by+c=0

    The point (-2,k) lies on the line L

    2) Find the value of k

    The line M has an equation y-x+12=0. Lines M and L intersect at point P.

    3) Find the coordinates of point P.
    1) Two known points on the line.
    First use the point-slope form (y-y1) = m(x-x1), then transform to the general form Ax +By +C = 0

    m = (y2 -y1)/(x2 -x1)
    m = (10 -4)/(2 -6) = 6/(-4) = -3/2
    y -4 = (-3/2)(x -6)
    Clear the fraction, multiply both sides by 2,
    2y -8 = -3x +18
    3x +2y -8 -18 = 0
    3x +2y -26 = 0 ----------answer.

    2) If point (-2,k) is on line L, then,
    3(-2) +2(k) -26 = 0
    -6 +2k -26 = 0
    2k = 6 +26 = 32
    k = 32/2 = 16 --------answer.

    3.)
    Line M is y -x +12 = 0
    Line L is 3x +2y -26 = 0
    If they intersect at point P, then their coordinates are the same at point P.
    Or, the y of line M equals the y of line L at point P.

    y -x +12 = 0
    y = x -12 -------y of line M anywhere.

    Substitute that into the equation of line L,
    3x +2(x -12) -26 = 0
    3x +2x -24 -26 = 0
    5x -50 = 0
    5x = 50
    x = 50/5 = 10 -----the x-coordinate of point P.
    Substitute that into the y of line M,
    y = 10 -12
    y = -2 ----the y-coordinate of point P

    Therefore, point P is (10,-2) --------answer.

    Check that on line M,
    y -x +12 = 0
    -2 -10 +12 =? 0
    0 =? 0
    Yes, so, OK.

    On line L,
    3x +2y -26 = 0
    3(10) +2(-2) -26 =? 0
    30 -4 -26 =? 0
    0 =? 0
    Yes, so, OK also.
    Last edited by ticbol; December 2nd 2005 at 12:04 PM.
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