Math

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If the point (x, y) is one-third of the way from (-2, 6) to (6,-8), then what is x + y?

What is the x+y?

  • Math -

    for the x:
    (x+2)/(6+2) = 1/3
    3x + 6 = 8
    3x = 2
    x = 2/3

    for the y:
    (y-6)/(-8-6) = 1/3
    3y - 18 = -14
    3y = 4
    y = 4/3

    (x,y) = (2/3,4/3)

    check: distance form (-2,6) to (2/3,4/3)
    = √( (-2-2/3)^2 + (6-4/3)^2
    = √( 64/9 + 196/3)
    =√(260/9)
    = (1/3)√260

    distance from (-2,6) to 6,-8)
    = √( 64 + 196)
    = √260

    so the distance checks out

    x+y = 2/3 + 4/3 = 6/3 = 2

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