Consider the line segment joining A(-1,2) and B(3,4)

a) find an equation that expresses the fact that a point P(x,y) is equidistant from A and from B.

b) describe geometrically the set of points described by the equation in part (a).

3 answers

a) arriving at the equation only using your definition for P .....
AP = BP
√( (x+1)^2 + (y-2)^2 ) = √( (x-3)^2 + (y-4)^2 )
square both sides and expand
x^2 + 2x + 1 + y^2 -4y + 4 = x^2 - 6x + 9 + y^2 - 8y + 16
8x - 12y = 20 or
2x - 3y = 5

b) of course the equation we found in a) is the right - bisector of AB

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