Which triangle has a point at its centroid?

A triangle has a point at its centroid, which is the point where the three medians of the triangle intersect. The centroid is often denoted as point \( G \) and is located at the average of the vertices' coordinates. For a triangle with vertices at points \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), the coordinates of the centroid \( G \) can be calculated using the following formula: \[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \] This means that every triangle, regardless of its type (scalene, isosceles, or equilateral), has a centroid. The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.