Xavier Aptitude Test 2011 Paper

Question : 51 of 101

Marks: +1, -0

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

1 + $√37$
$5√ 2 + 2√ 10$
$√41 +√ 37$
$√41$ + 1
None of the above

Validate

Solution:

(a) For PL

+\ {PN}

to be minimum. P should lie on LN.
Similarly, for

\ {PO}+\ {PM}

to be minimum P should lie on

\ {OM}

\∴\ {P}

is the intersection of the diagonal OM and LN.

( {PL}+\ {PM}+\ {PN}+\ {PO}) _{\min}

=(\ {PL}+ {PN})_{\min }+ ( {PO}+\ {PM})_{\min }

=\ {L} \ {N}+\ {OM}

=5 \√{2}+2 \√{10}

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