The problem is your derivative, it has to be:
It is given that y = 0.5(x^2) 3x + 12
The points P and Q on the graph have x-coordinates 0 and 8 respectively. The tangents at P and Q meet at R. Show that the point (11, 9) is equidistant from P, Q and R.
Alright so this is my work so far:
dy/dx = 2x 3
P (0, 12), Q (8, 20)
Equation of tangent at P: (y 12)/(x 0) = -3 => y = 12 - 3x
Equation of tangent at Q: (y 20)/(x 8) = 13 => y = 13x - 84
Point of intersection R is defined by: 12 3x = 13x 84 => 16x = 96 => x = 6
R(6,-6)
Distance between (11, 9) and P = sqrt((11^2) + (-3^2)) = sqrt(130)
Distance between (11, 9) and Q = sqrt((3^2) + (-11^2)) = sqrt(130)
Distance between (11, 9) and R = sqrt(((11-6)^2) + ((9+6))^2) = sqrt(250)
So theres my problem. Where have I messed up?