Question

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?

Answer 1

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 open-ended.

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

(2x-3)^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).

Answer 2

Oops. The diameter is √34, not the radius.