I'm having trouble finding the centroid of a triangle algebraically. I have the midpoints and I also have the median equations, I just don't know how to get their point of intersection.

Question

klimenkov · Answer

Write these equations here.

anonymous · Answer

The vertices are A(4,14) B(14,7) and C(2,4). The equations are: 
AD: y=-17/8x+45/2 
CF: y=13/14x+15/7 
EB: y=-2/11x+105/11
AD, CF, and EB are the Medians. I need to find their point of concurrence

anonymous · Answer

if all of these lines intersect each other, you just need to solve the linear system with any two of these equation

anonymous · Answer

Oh!

anonymous · Answer

so I could just do -17/8x+45/2=13/14x+15/7 and that would give me the x, and then I just solve and find the y?

anonymous · Answer

that's it!

anonymous · Answer

Thank you soo much, that's a lot simpler than I thought!

anonymous · Answer

then you can plug this x value in all of the three equations and you will see that will return the same y value

klimenkov · Answer

Actually, if you have the vertices, you do not need these equations.
The centroid will be $\frac{A+B+C}{3}$.

anonymous · Answer

My teacher actually won't let us use that equation, but thank you!

anonymous · Answer

That is right @klimenkov , that is the most used way to find the centroid