Precalculus

posted by Mark

Considering the line segment joining A(-5, 2) and B(7, 8), find an equation, in the form of Ax+By=C, that expressed the fact that a point P(x, y) is equidistant from A and from B. How would I go about even attempting this problem?

  1. Damon

    any point on the perpendicular bisector of AB satisfies your requirement.

    what is the slope of AB ?
    slope = (8-2)/(7+5) = 6/12 = 1/2
    so the perpendicular has slope
    m = -2
    It must go through the midpoint of AB which is at:
    x =(7-5)/2 = 1
    y = (8+2)/5 = 2
    or (1,2)
    so
    2 = -2(1) + b
    b = 4
    so
    y = -2 x + 4
    2 x + y = 4

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