math 1

The vertices J(2,6), K(7,8), L(9,3), and M(?, ?) determine a square. Show your work to find the coordinates of M. Use complete sentences and proper grammar to give a justification why JKLM is a square.

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  1. let the fourth vertex be M(x,y)
    slope KJ = slope LM
    2/5 = (y-3)/(x-9)
    2x - 18 = 5y - 15
    2x - 5y = 3 #1

    slope JP = slope LM
    (y-6)/(x-2) = -5/2
    2y - 12 = -5x + 10
    5x + 2y = 22 #2

    #1 times 2 ---> 4x - 10y = 6
    #2 times 5 ---> 25x + 10y = 110
    add them:
    29x = 116
    x = 4
    back into #2
    20 + 2y = 22
    y = 1

    M is (4,1)

    check my arithmetic

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