question_answer

The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line \[y=2x+c,\] then the value of c will be                 [Pb. CET 2003; IIT 1981]

A)            4    

B)            - 4

C)            2    

D)            - 2

Correct Answer: B

Solution :

           Let ABCD be a rectangle. Given A (1, 3) and C (5, 1). Equation B and D lie on \[y=2x+c\]                    We know that intersecting point of diagonal of rectangle is same or at midpoint. So mid point of AC is (3, 2). So \[y=2x+c\] passes through (3, 2). Hence\[c=-4\].