Question

if A(-2,1) B(9,0) C (4,b) and D(1,2) are the verticles of a parallelogram ABCD, find the value of a and b. hence find the lenght of its sides.

Answer 1

Hii friend,


ABCD IS A PARALLELOGRAM.

SIDES OF PARALLELOGRAM AB , BD, AC, CD

A(-2,1) , B(9,0) , C(4,B) , D(1,2).

AD AND BC ARE THE DIAGONALS OF PARALLELOGRAM.

WE KNOW THAT,

THE DIAGONALS OF PARALLELOGRAM BISECT EACH OTHER AT O.

O IS THE MIDPOINT OF DIAGONALS AD AND BC.

THEREFORE,

THE COORDINATES OF O IS = X1+X2/2 , Y1+Y2/2.

= (-2+1/2 , 1+2/2 ) = (-1/2, 3/2).

AND,

O IS THE MIDPOINT OF BC.

THEREFORE,

COORDINATES OF POINT OF = X1+X2/2 , Y1+Y2/2.

= (9+4/2, 0+b/2

= (13/2, b/2) ARE THE COORDINATES OF POINT O.

BUT ,

THE COORDINATES OF POINT O IS O(-1/2),(3/2).

THEREFORE,

b/2 = 3/2

2b = 6

b = 6/2 = 3.