Geometry

Find the coordinates of the orthocenter of the triangle with the given vertices.
L (8,0) M (10,8) N (14,0)

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  1. The orthocentre is the intersection of the altitudes of a triangle.
    You will need the equation of two of these and find their intersection

    Make a sketch:
    notice that LN lies on the x-axis, so the altitude from M is simply x = 10
    that was too easy.

    let's find the altitude to MN
    slope of MN = (8-0)/(10-14) = -2
    so slope of altitude is 1/2
    and passing through (8,0)
    0 = (1/2)(8) + b
    b = -4
    thus y = (1/2)x - 4
    but x = 10
    then y = (1/2)(10) - 4 = 1

    the orthocentre is (10,1)

    As an additional check, find the remaining altitude and verify by subbing in (10,1)

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