what is a locus of points
Locus. From Latin: locus - place. Definition: A shape created by the set of points whose position satisfies a given set of rules. Try this In the figure below, the small gray dots represent all the possible points on the plane.
Therefore, when K is in the present case of the unit equilateral triangle, the locus is a single point. When K = 2, each of the vertices is part of the locus, and further, no point on the interior of the triangle is part of the locus. A Geometrer's SketchPad drawing produced the following estimates of points on the locus when the length of a+b+c was about 1.9.