MathNet 2015-part-07 — 185 problems (EN–VI) Question 117

Let $ABCD$ be a quadrilateral with $A=(3,4)$, $B=(9,-40)$, $C=(-5,-12)$, $D=(-7,24)$. Let $P$ be a point in the plane (not necessarily inside the quadrilateral). Find the minimum possible value of $AP + BP + CP + DP$.