Q 1224045851.     Following points `(1, 3)` and `(5, 1)` are two opposite vertices of a rectangle. The other two vertices lie on the line `y = 2x + c`. Find `c` and the remaining vertices.

JEE 1978
A

`c = - 8` , vertices are `( 8, 8 ), ( 8, 1 )`

B

`c = - 4` ,vertices are `( 4, 4 ), ( 2, 0 )`

C

`c = - 6`, vertices are `( 6, 6 ), ( 4, 0 )`

D

`c = - 7`, vertices are `( 7, 7 ), ( 9, 0 )`

HINT

diagonal of rectangle bisect each other, so mid-point of `( 1, 3 )` and `( 5, 1 )` must satisfy `y = 2x + c` .

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