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11th

Maths

Straight Lines

Introduction

If A( - 2, 1), B(a, 0), C(4...

MATHS

If A(−2,1),B(a,0),C(4,b) and D(1,2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

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ANSWER

Given sides of parallelogram A(−2,1),B(a,0),C(4,b),D(1,2)

We know that diagonals of Parallelogram bisect each other. 

Mid-point let say  O of diagonal AC is given by 

x=(2x1+x2)and y=(2y1+y2)

O  (2−2+4,21+b) ..................(1)

Mid-point let say  P of diagonal BD is given by 

P  (2a+1,20+2) ..................(2)

Points O and P are same 

Equating the corresponding co-ordinates of both midpoints, we get

2−2+4