Q. 64.3( 10 Votes )

# 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)

Answer :

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 (x_{3}, y_{3}).

And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x_{1}, y_{1}) and (x_{2}, y_{2}) is

(Where, (x_{1}, y_{1}) and (x_{2}, y_{2}) are the coordinates of A and C

Now, Let the co-ordinates of mid-point of BD be (x_{4}, y_{4}).

And, since it is a mid-point –

(Where, (x_{5}, y_{5}) and (x_{6}, y_{6}) 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 –

⇒ x_{4} = x_{3} and y_{4} = y_{3}

⇒ x = 9 and y = 6.

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