Asked by Andrea
                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).
            
        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).
Answers
                    Answered by
            Reiny
            
    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
    
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
                    Answered by
            Jason
            
    THAAAAAAANK YOOOOOOU.
    
                    Answered by
            Andrea
            
    yeah, thank you!
    
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