How do i find the centroid of this this triangle

i need to find the centroid of triangle ABC A(1,0) B(11,2) C(7,4). it has to be the long wat not the x1+x2+x3/3 thing. I already have the midoints AB(6,1) BC(9,3) AC(4,2). Please help im really confused on were to go from there

You have the correct midpoints. Now you need to determine the equations of
two of the medians, then find their point of intersection.

So with AB(6,1) and C(7,4), this median has slope (4 - 1)/(7 - 6) = 3, so the equation
of the median line will be y - 1 = 3*(x - 6) ----> y = 3x - 17.

With BC(9,3) and A(1,0), this median has slope (0 - 3)/(1 - 9) = 3/8, so the equation
of the median line will be y = (3/8)*(x - 1).

So these two medians intersect when 3x - 17 = (3/8)*(x - 1) ---->

24x - 136 = 3x - 3 ----> 21x = 133 ----> x = 133/21 = 19/3, and thus

y = 3*(19/3) - 17 = 2. So the centroid is at (19/3, 2).