# 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.

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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