Question

One of the diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7.

If A and B are the points (–3, 4) and (5, 4) respectively, then the area of rectangle is-

• A. 40 sq. units
• B. 32 sq. units
• C. 30 sq. units
• D. 16 sq. units

Answer 1

Answer: (B)

32 sq. units

Answer 2

First, we note that none of the points A (–3, 4) B(5, 4) lie on the diameter 4y = x + 7

Let E (a, b) be the centre of the circle,

then 4b = a + 7 … (i)

Since ABCD is a rectangle |EA| = |EB| Ю EA² = EB²

Ю (a + 3)² + (b – 4)² = (a –5)² + (b –4)²

Ю 6a + 9 = – 10a + 25

Ю a = 1, and from (i) b = 2

Now |AB| = $\sqrt{(5 + 3)^{2} + (4 - 4)^{2}}$= 8 and |BD| = 2|EB| = 2$\sqrt{(5 - 1)^{2} + (4 - 2)^{2}}$=4$\sqrt{5}$

From right Рd D ABD, AD² = BD² –AB²

= 80 –64 = 16

Ю |AD| = 4,

\ Area of the rectangle ABCD = |AB|. |AD|

= 8.4 = 32 sq. units.