geometry (maths)

ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpendicular AC.

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  1. let AB = x
    then BC = 2x
    CE = 2(2x) = 4x

    slope BE = 4x/(2x) = 2
    slope AC = -x/(2x) , negative since it leans to the left
    = -1/2

    since 2 is the negative reciprocal of -1/2,
    BE and AC are perpendicular.

    or

    place rectangle ABCD on the x-y grid with B at the origin.
    A is (0,x)
    B is (,0)
    C is (2x, 0)
    D is (2x, x)
    E is (2x, 4x)

    find slope BE and slope AC to show the same result

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