Point Z is the centroid of the triangle, which means it is the point of intersection of the medians of the triangle. The centroid divides each median into two segments, with the longer segment being twice as long as the shorter segment. This relationship can be justified by the Concurrency of Medians Theorem, which states that the three medians of a triangle intersect at a point (the centroid) that is two-thirds of the distance from each vertex to the midpoint of the opposite side. In other words, point Z is the balancing point of the triangle, where all three medians intersect and divide each other in the same ratio.
