document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #767062 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "(1)  Since the epicenter is equally remoted from the points X and Y, the epicenter lies on the perpendicular bisector \r\n" );
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document.write( "     to the segment XY on the coordinate plane.\r\n" );
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document.write( "(2)  So, write the equation of the straight line bisecting this segment.\r\n" );
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document.write( "     It is ELEMENTARY.\r\n" );
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document.write( "(3)  The epicenter lies at the intersection point of the straight line determined in (2), and the circle of the radius of 5\r\n" );
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document.write( "      centered at Z.\r\n" );
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document.write( "(4)  So, write these two equations for the straight line and for the circle as a system and then solve it.\r\n" );
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document.write( "(5)  The solution/solutions of the system is the epicenter.\r\n" );
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document.write( "     There are two possible cases:  the two solutions represent two intersection point or one, if two solutions merge into one.\r\n" );
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document.write( "     I don't know which of the two cases will really be realized;\r\n" );
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document.write( "     but when you complete the solution, you will know.\r\n" );
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