Q. 383.7( 3 Votes )

The three vertices of a rectangle ABCD are A(3, 2), B(–2, 2) and C(3, –3). Plot these points on a graph paper and find the coordinates of D. Also, find the area of rectangle ABCD.

Answer :

Let the three vertices of rectangle ABCD be A (3, 2), B (-2, 2) and D (3, -3)

Now, on plotting these points on the graph paper and by joining the points we get:



A, B and D lie in different quadrants


Let us assume D be the fourth vertex of the rectangle


Abscissa of C = Abscissa of B = - 2


And, Ordinate of C = Ordinate of D = - 3


Hence, Coordinate of the fourth vertex, C = (-2, -3)


Let y-axis cut AB and CD at point L and M respectively


AB = (BL + LA)


= (2 + 3)


= 5 units


Area of rectangle ABCD = AB × AB


= 5 × 5


= 25 square units


Hence, the area of the rectangle ABCD is 25 square units


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