Question

Two points $(a,3)$ and $(5,b)$ are the opposite vertices of a rectangle. If the other two vertices lie on the line $y=2x+c$ which passes through the point $(a,b)$ then the value of $c$ is

• A. $-7$
• B. $-4$
• C. $0$
• D. $7$

Answer 1

The correct option is A $-7$

Mid-point of the line joining the given points lie on the given line

$\therefore \frac{3+b}{2}=2\left(\frac{a+5}{2}\right)+c$ $\Rightarrow 2a+2c-b+7=0$ ...(1)

Also, since the given line passes through $(a,b)$

$b=2a+c$ ...(2)

Solving (1) and (2), We get $c=-7$