Geometry
posted by Mirielle .
In right triangle abc, c is the right angle. If the coordinates of A are (1,1) and the coordinates of B are (4,2). the coordinates of c maybe?

All we have is the hypotenuse AB.
Any point C on a circle with AB as a diameter will have a right angle at C.
So, unless they have given you choices, or otherwise placed conditions on C, it's pretty openended.
Since the center of the circle is (3/2,1/2), and the radius of the circle is √34, the equation of the circle is
(2x3)^2 + (2y+1)^2 = 34
Naturally, if the triangle has legs parallel to the axes, then obvious choices for C are (4,1) and (1,2). 
Oops. The diameter is √34, not the radius.
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