If the parallel sides of a trapezium are 8 cm and 4 cm M and N are the mid points of the diagonals o...........

Quantitative Aptitude (CGL) Coordinate Geometry

If the parallel sides of a trapezium are 8 cm and 4 cm, M and N are the mid points of the diagonals of the trapezium, then length of MN is

12 cm

6 cm

1 cm

2 cm

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Explanation:

CONSTRUCTION: Through N , construct NP // AB .
In triangle CAB, Since NP // AB ( const)
& N is mid point of AC ( given)
So, 'P' should be the mid point of BC & also NP = AB/2 ( by mid point theorem)
ie NP= 2 cm
Now Since , NP// AB. But AB// DC ( trap)
=> DC // PN or extended PN
But P is the mid point of BC
=> Extended PN passes through the mid point of DB ( mid point theorem)
=> mid point of DB coincides with M ( as it's given that M is the mid point of DB)
Hence, MP = DC/2
=> MP = 4 cm
& MN = MP - NP
=> MN = 4 - 2
MN = 2 cm