Q. 305.0( 1 Vote )

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

Answer :

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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