# Where is the centroid?

**Geometry**Level 3

A triangle has its vertices on the points \(A(2,4), B(8,-2)\) and \(C(9,9)\). The coordinate of this triangle's centroid is \(\left(\dfrac{a}{c},\dfrac{b}{c}\right)\), where \(a\), \(b\) and \(c\) are coprime integers. Find \(a+b+c\).

**Bonus**: Generalize the solution to find the centroid of a triangle.