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)
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.
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