Question

In a plane rectangular coordinate system, points L, M, N and O are represented by the coordinates (-5, 0), (1,-1), (0, 5), and (-1, 5) respectively. Consider a variable point P in the same plane. The minimum value of PL + PM + PN + PO is

Accepted Answer

B. The minimum distance sum $PL + PN + PM + PO$ for a convex quadrilateral $LMNO$ is equal to the sum of lengths of the diagonals $LN + OM$. $LN = \sqrt{(0 - (-5))^2 + (5 - 0)^2} = \sqrt{25 + 25} = 5\sqrt{2}$. $OM = \sqrt{(1 - (-1))^2 + (-1 - 5)^2} = \sqrt{4 + 36} = \sqrt{40} = 2\sqrt{10}$. Minimum value $= 5\sqrt{2} + 2\sqrt{10}$.

Coordinate Geometry: Minimum Distance Sum

Explanation

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