1. ln 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
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By: anil on 05 May 2019 02.37 am
$$(PL + PN)$$ will be minimum if P lies on PN, and $$(PM + PO)$$ will be minimum if P lies on OM. => P must be the intersection point of the diagonals of the quadrilateral. $$ herefore$$ Min (PL + PM + PN + PO) = $$LN + OM$$ = $$(sqrt{(0 + 5)^2 + (5 - 0)^2}) + (sqrt{(1 + 1)^2 + (-1 - 5)^2})$$ = $$(sqrt{25 + 25}) + (sqrt{4 + 36})$$ = $$sqrt{50} + sqrt{40} = 5 sqrt{2} + 2 sqrt{10}$$
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