If the point s (3, 2), (6, 3), (x, y) and (6, 5) when joined in order and form a parallelogram, then let us calculate the point (x, y)

Let A (3, 2), B (6, 3), C (x, y) and D (6, 5) We know that a quadrilateral is a parallelogram if the co-ordinates of mid-point s of its both the diagonals are same.

Therefore, we’ll use the mid-point s of diagonal AC and BD.

Let the co-ordinates of mid-point of AC be (x₃, y₃).

And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x₁, y₁) and (x₂, y₂) is

(Where, (x₁, y₁) and (x₂, y₂) are the coordinates of A and C

Now, Let the co-ordinates of mid-point of BD be (x₄, y₄).

And, since it is a mid-point –

(Where, (x₅, y₅) and (x₆, y₆) are the coordinates of B and D.

⇒x = 6 and y = 4

⇒ Co – ordinates of mid-point of BD =

And, since it is a parallelogram –

⇒ x₄ = x₃ and y₄ = y₃

⇒ x = 9 and y = 6.