Q29 of 184 Page 10

If (6,8), (3,7) and (-2,-2) be the coordinates of the three consecutive vertices of a parallelogram, find coordinates of the fourth vertex.


Let the coordinates of the fourth vertex D be (x, y).


We know that diagonals of a parallelogram bisect each other.


∴ Midpoint of AC = Midpoint of BD …(i)


Coordinates of the midpoint of AC are



Coordinates of the midpoint of BD are



So, according to eq. (i), we have




⇒ 3 + x = 4 and 7 + y = 6


⇒ x = 1 and y = -1


Thus, the coordinates of the vertex D are (1, -1)


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