Given a triangle, what is the equation of the line which bisects its area and has a given slope? The set of all lines bisecting the area of a triangle has been elegantly determined as a certain ‘deltoid’ envelope and this gives an indirect method of solution. We find that vector algebra allows the equation to be written down rather directly and neatly.

It is well known that amedian of a triangle divides it into two triangles of equal area, and that the three medians meet at the centroid. Hence, every triangle has at least one point through which… Expand