Analytic Geometry

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A point is equidistant from (-2,4) and (3,5). It is also equidistant from (-2,-3) and (6,-1). Find the point



Please I need Help with this

  • Analytic Geometry -

    The point must be on the right-bisector of the line segment from (-2,4) to (3,5)

    slope of line segment is 1/5, so slope of right-bisector is -5
    midpoint of line segment is (1/2 , 9/2)

    equation of right-bisector of line segment is
    y - 9/2 = -5(x - 1/2)
    2y - 9 = -10x + 5
    10x + 2y = 14
    5x + y = 7 or y = -5x+7

    2nd line segment:
    slope of line segment = 2/8 = 1/4
    slope of right-bisector = -4
    midpoint = (2, -2)
    equation of right-bisector
    y+2 = -4(x-2)
    y +2 = -4x+8
    y = -4x + 6

    then:
    -4x+6 = -5x+7
    x = 1
    which makes y = -4(1)+6 = 2

    the point is (1,2)

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