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March 27, 2017

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The (x,y) is equidistant from (0,0) and (4,-2). Find its algebraic equation.

  • analytic geometry - ,

    must be on the right bisector of the line joining (0,0) and 4,-2)

    slope of that line is (-2-0)/(4-0) = -1/2
    so the slope of the right-bisector must be +2
    and we can start by saying the equation of the right-bisector must be
    y = 2x + b

    but we also know that the mid point of our line segment must lie on this
    midpoint = ((4+0)/2 , (-2+0)/2 ) = (2, -1)

    so in y = mx + b
    -1 = 3(2) + b
    b = -7

    y = 2x - 7

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