Geometry

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The points A,B,C,D have coordinates (3,3) (8,0) (-1,1) (-6,4) respectively.

Find the coordinates of the point of intersection of the diagonals AC and BD?


Help plZ!!!

  • Geometry -

    You will have to find the equation of both diagonals

    I will do AC , using the points (3,3) and (-1,1)
    slope of AC = (3-1)/(3+1) = 2/4 = 1/2

    then again using (3,3)
    y-3 = (1/2)(x-3)
    2y - 6 = x-3
    x - 2y = -3

    Now you find the equation for BD
    then solve the two equations.

  • Geometry -

    I get the gradient part reiny, but how do you use one of the points to get the equation?

  • Geometry -

    The gradient/slope for BD is -2/7

  • Geometry -

    Ah wait i got the equation for BD as

    y=-2/7 x + 16/7

    is that right?

  • Geometry -

    Maybe you use y = mx + b

    then y = (1/2)x + b
    sub in (3,3)
    3 = (1/2)(3) + b
    b = 3 - 3/2
    b = 3/2

    y = (1/2)x + 3/2

    suppose I multiply each term by 2 to get

    2y = x + 3
    re-arrange for x - 2y = -3 , the same as I had before, but much easier and faster

    The method of y = mx + b seems to be the one taught most often these days, but personally, I would hardly ever use it if my slope is a fraction.
    If the slope is an integer, then it makes sense to use
    y = mx + b

  • Geometry -

    Yes, your second equation is correct

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