SOLUTION: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(15,8), (-9,-2), and (-1,6) respectively. The epicenter of an earthquake is determ

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Question 1145647: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(15,8), (-9,-2), and (-1,6) respectively. The epicenter of an earthquake is determined to be 13 units from X​, 13 units from​ Y, and 5 units from Z. Where on the coordinate plane is the epicenter​ located?
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

            I only will give instructions on what to do and how to solve the problem, leaving all details to you . . . 


(1)  Since the epicenter is equally remoted from the points X and Y, the epicenter lies on the perpendicular bisector 

     to the segment XY on the coordinate plane.



(2)  So, write the equation of the straight line bisecting this segment.

     It is ELEMENTARY.



(3)  The epicenter lies at the intersection point of the straight line determined in (2), and the circle of the radius of 5

      centered at Z.



(4)  So, write these two equations for the straight line and for the circle as a system and then solve it.



(5)  The solution/solutions of the system is the epicenter.


     There are two possible cases:  the two solutions represent two intersection point or one, if two solutions merge into one.


     I don't know which of the two cases will really be realized;

     but when you complete the solution, you will know.

At this point, I complete my instructions and leave the implementation to you.



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