Q30 of 184 Page 10

Three consecutive vertices of a rhombus are (5,3), (2,7) and (-2,4). Find the fourth vertex.


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


We know that diagonals of a rhombus 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




⇒ 2 + x = 3 and 7 + y = 7


⇒ x = 1 and y = 0


Thus, the coordinates of the vertex D are (1, 0)


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