<PRE><B>Question 1195338</B>
&lt;br&gt;
Because AC=BC, point C is on the perpendicular bisector of segment AB.  So find the equation of that perpendicular bisector and then solve the pair of linear equations to find the coordinates of C.&lt;br&gt;
AB has slope (-3-1)/(6-(-2)) = -1/2 and midpoint (2,-1).&lt;br&gt;
The perpendicular bisector has slope 2 and passes through (2,-1); its equation is y=2x-5, or 2x-y-5 = 0.  So we have&lt;br&gt;
(1) 4x-7y+15 = 0
(2) 2x-y-5 = 0&lt;br&gt;
Double the second equation and subtract one equation from the other to find y:&lt;br&gt;
4x-7y+15 = 0
4x-2y-10 = 0&lt;br&gt;
-5y+25 = 0
5y = 25
y = 5&lt;br&gt;
Substitute y=5 in either equation to find x:&lt;br&gt;
2x-5-5 = 0
2x-10 = 0
2x = 10
x = 5&lt;br&gt;
ANSWER: C is (5,5)&lt;br&gt;
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