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The points A(1, 3) and C(5, 1) are extremities of a diagonal of a rectangle ABCD. The other two vertices B and D lie on the line y = 2x + c. Then, the value of c is

(a)  2

(b)  4

(c)  -4

(d)  -2

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orrect option  (B)  -4

Explanation :

See Fig. Let M = (3, 2) be the intersection of the diagonals. Since M(3, 2) lies on the diagonal BD whose equation is given as y = 2x + c, we have

2 = 2(3) + c

c = -4

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