Three Points Equidistant...

So I thought I knew how to solve this kind of question, but apparently not.

Find a point equidistant from the three points, P(3, 2), Q(3, -3), R(-2, 2).

My (wrong) answer: Mid-point of PQ is (3, -1/2), so the slope of the line from R to this point is (-5/2)/5 = -1/2. Going two to the right from R by this slope, we go down to 1, so the equation of the line is y = (-1/2)x + 1.

Mid-point of PR is (1/2, 2), so the slop of the line from this point to Q is -5/(5/2) = -2. Going from this point, one-half unit to the left we go up one, so the equation of the line is y = -2x + 3.

Now I want to find the point of intersection between these two lines, so I set them equal to each other and solve for x, giving me x = 4/3, which is wrong.