IIT JEE , AIEEE Forum - Mathematics , Algebra

nishant_delhi

Q. show that :

(-1,2,1),(1,-2,5),(4,-7,8) & (2,-3,4) are the vertices of a parallelogram .

(explain briefly...........rate assured)

priyesh

let the vertices be A(-1,2,1) B(1,-2,5) C(4,-7,8) & D(2,-3,4)

midpt of AC = (3/2,-5/2,9/2) (using midpt formula)

similarly

midpt of BD = (3/2,-5/2,9/2)

hence AC & BD bisect each other so the quadrilateral is a parelleogram with diagnals AC & BD

(using property that if in a quad. diagnals bisect each other it is a parellelogram)