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?
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