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+1 vote
933 views
in Mathematics by (53.1k points)

One of the diameters of the circle circumscribing the rectangle ABCD is x - 4y + 7 = 0. If A = (-3, 4) and B = (5, 4), then the area of ABCD is

(A)  72 

(B)  64 

(C)  32

(D)  36

1 Answer

+2 votes
by (53.3k points)
selected by
 
Best answer

Correct option (C) 32 

Explanation :

Let P(h, k) be the centre and Q(1, 4) be the midpoint of AB (see Fig) Since AB is a horizontal segment, it follows that PQ is vertical. Therefore, h = 1 and h 4k + 7 = 0  k =2. Hence, the centre of the circle is (1, 2). It is clear that BC = 2PQ which implies that

BC = 2(2) = 4 

Now AB = 8 and BC = 4 which implies that 

Area of ABCD = 8 x 4 =  32

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