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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