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A quadrilateral has vertices (4,1), (1,...

A quadrilateral has vertices `(4,1), (1,7),(-6,0)` AND `(-1,-9)`. Show that mid-points of the sides of this quadrilateral form a parallelogram.

Text Solution

Verified by Experts

Mid point of PR`=(((5/2)+(-7/2))/2,((4+(-9/2))/2)`
`=(-1/2,-1/4)`
MId point of SQ`=(((3/2)-(5/2))/2),((-4+(7/2))/2)`
`=(-1/2,-1/4)`
`PQ=sqrt(5^2+(1/2)^2)=sqrt(25+1/4)=sqrt(101/4)`
`SR=sqrt(5^2+(1/2)^2)=sqrt(25+1/4)+sqrt(101/4)`
`RQ=sqrt((-7/2+5/2)^2+(-9/2-7/2)^2)=sqrt65`
`SP=sqrt((3/2-5/2)^2+(-8)^2)=sqrt65`
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