Question

Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.

Answer 1

The given points of the parallelogram are A(3, 1), B(5, 1), C(a, b) and D(4, 3). 

We know that the diagonals of a parallelogram bisect each other. So, O is the midpoint of AC and DB. 

So, 
`((3+"a")/2 ,(1+"b")/2) =((5+4)/2, (1+3)/2)`

⇒ `((3+"a")/2 ,(1+"b")/2) = (9/2,4/2)`

⇒ `((3+"a")/2 ,(1+"b")/2) = (9/2,2)`

On comparing we get

`(3+"a")/2  =9/2`

⇒ 3 + a = 9

⇒ a = 6

Also,

`(1+"b")/2 = 2`

⇒ 1 +b = 4

⇒ b = 3

Thus , a = 6, b = 3