Q. 54.3( 13 Votes )
Prove that when the point s A (7, 3), B (9, 6), C (10, 12) and D (8, 9) are joined in order, then they will form a parallelogram.
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 find 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
⇒ Co – ordinates of mid-point of AC =
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.
⇒ Co – ordinates of mid-point of BD =
And, since these are equal –
⇒ ABCD is a parallelogram.
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