calculate centroid of triangle on a graph Given ANY three points on a graph that form a triangle, how do you find the centroid using geometry? So basically I have three points (X1, Y1), (X2, Y2), and (X3, Y3). I am trying to use the slopes between opposing points to find the centroid but I am currently stuck. I'm not sure how to use geometry/algebra to solve for the centroid coordinates exactly without integration. Thanks!

Given three points in the coordinate plane $p_1 = (x_1,y_1)$, $p_2=(x_2,y_2)$, and $p_3=(x_3,y_3)$, the coordinates of the centroid $q$ is simply the average of the coordinates of the three points (actually, this is sometimes how the centroid is defined):
$$q = \left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$$
