This illustrates the fact that every point in the triangle $abc$ can be expressed as $ua+vb+wc$ for some coefficients $u,v,w\geq 0$ such that $u+v+w=1$. In fact, every point in the plane can be expressed in this way, except that one or more of the coefficients will be negative if the point lies outside the triangle. On each side of the triangle, one coefficient becomes zero. At each vertex of the triangle, two of the coefficients are zero and the third is equal to one.

You can hover over the triangle to see the coordinates, or click and drag the corners to change the triangle.