Question

If (-2,-1) , (a,0) , (4,b) and (1,2) are the vertices of a parallelogram, find the values of a and b.

Answer 1

Hii friend,

Let A(-2,-1) , B(a,0) , C(4,b) and D(1,2) be the vertices of a parallelogram ABCD . join AC and BD , interesting each other at O.

We know that the diagonals of a parallelogram bisect each other.

Therefore,

O is the midpoint of AC as well as BD.

Midpoint of AC = (-2+4/2 , -1+b/2) = (1,b-1/2 ).

Midpoint of BD = (a+1/2 , 0+2/2) = (a+1/2 , 1).

Therefore,

a+1 /2 = 1. and b-1/2 = 1

a+1 = 2. and b-1 = 2

a = 2-1. and b = 2+1

a = 1. and b = 3

Hence,

a= 1 and b = 3


HOPE IT WILL HELP YOU..... :-)

Answer 2

hy
here is your answer
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Let A(-2,-1) , B(a,0) , C(4,b) and D(1,2) be the vertices of a parallelogram ABCD .

join AC and BD , interesting each other at O.


We know that the diagonals of a parallelogram bisect each other.

Therefore,


O is the midpoint of AC as well as BD.


Midpoint of AC = (-2+4/2 , -1+b/2) = (1,b-1/2 ).


Midpoint of BD = (a+1/2 , 0+2/2) = (a+1/2 , 1).


Therefore,


a+1 /2 = 1. and b-1/2 = 1


a+1 = 2. and b-1 = 2


a = 2-1. and b = 2+1


a = 1. and b = 3


Hence,

a= 1 and b = 3