If A, B, C are collinear points, A = (3,4), B = (7,7) and AC = 10 then C =

A(3,4), B = (7,7), AC =10, $\Rightarrow AB=\sqrt{16+9}=\sqrt{25}=5$, B is divides in the ratio AC is 1 : 1 

$\Rightarrow B=\frac{A+C}{2}$

2(7, 7) = (3, 4) + (x + y)

$\Rightarrow 3+x=14\Rightarrow 4+y=14\Rightarrow x=11\Rightarrow y=10$