Figure 4
When the point P coincides with the centroid G of the triangle ABC the
ratio of the areas is a minimum of 4.00. This makes sense because when
point P coincides with the centroid C the segments DE, EF, & FD
form the medial triangle for triangle ABC. The area of the medial
triangle has 1/4 the area of triangle ABC, therefore the ratio at this
point will be 4, and as point P moves away from the centroid G the area
of triangle DEF gets smaller so the ratoi will increase.