To find the point of intersection of the medians of triangle ABC, we can use the fact that the medians of a triangle intersect at a point that is two-thirds of the way from each vertex to the midpoint of the opposite side. We can find the coordinates of the midpoint of each side of the triangle, and then use those coordinates to find the coordinates of the point of intersection of the medians.
The midpoint of side AB is:
((-2 - 1)/2, (0 + 6)/2) = (-1.5, 3)
The midpoint of side AC is:
((-2 + 6)/2, (0 + 0)/2) = (2, 0)
The midpoint of side BC is:
((-1 + 6)/2, (6 + 0)/2) = (2.5, 3)
Now, we can find the point of intersection of the medians by averaging the x-coordinates and y-coordinates of the midpoints of the sides:
(x-coordinate) = (-1.5 + 2 + 2.5)/3 = 1
(y-coordinate) = (3 + 0 + 3)/3 = 2
Therefore, the point of intersection of the medians is (1, 2).