coordinate geometry

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the three points g(4,0) ,h(h,6) and i(7,1) are such that gh is twice as long as gi .calculate the two possible values of h.

  • coordinate geometry -

    gi^2 = 3^2+1^2 = 10^2

    gh^2 = 4 * 10^2

    4*10^2 = (h-4)^2 + 36

    400 = h^2 - 8h + 36

    h^2 - 8 h - 364 = 0

    h = [ 8 +/- sqrt(64+1456) ]/2

    h = 4 +/- 19.5

    h = 23.5 or -15.5
    check my arithmetic !

  • coordinate geometry -

    using distance formula

    d of GI= square root of 10-3.1622

    twice this is the square root of 40

    could be- 6 or 2

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