SOLUTION: locate the point equidistant from A = (3,8), B = (5,2) and C = (-3,-4)

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Question 1184233: locate the point equidistant from A = (3,8), B = (5,2) and C = (-3,-4)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
A, (3,8)
B, (5,2)
C, (-3,-4)
unknown point, P, (x,y)


Setup equations using Distance Formula, and solve the system.


Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.


There is a standard algebraic and there is a standard geometric procedures to find that point.


            (1)   Geometric procedure 


Construct the perpendicular bisector to the segment AB.


Construct the perpendicular bisector to the segment BC.


Take the intersection point: it is EQUIDISTANT from the three given points A, B and C.


            (2)   Algebra procedure 


Write equation of the straight line which is the perpendicular bisector of the segment AB.


Write equation of the straight line which is the perpendicular bisector of the segment BC.


Solve the system of the two equation to find the intersection point: : it is EQUIDISTANT from the three given points A, B and C.



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