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Let square PQRS be a quadrilateral. If M...

Let `square PQRS` be a quadrilateral. If M and N are the mid-points of the sides PQ and RS respectively, then PS+QR=

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Let `bar(p),bar(q),bar(r),bar(s),bar(m)` and `bar(n)` be the position vectors of the points P,Q,R, S,M and N respectively. M and N are the midpoints of PQ and RS respectively.

`:.bar(m)=(bar(p)+bar(q))/(2)andbar(n)=(bar(r)+bar(s))/(2)`
`:.bar(PS)+bar(QR)=(bar(s)-bar(p))+(bar(r)-bar(q))`
`=bar(s)-bar(p)+bar(r)-bar(q)`
`=2((bar(r)+bar(s))/(2))-2((bar(p)+bar(q))/(2))`
`=2bar(n)-2bar(m)`
`=2(bar(n)-bar(m))" ":.bar(PS)=bar(QR)=2MN`.
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