Question

The points $(2,5)$ and $(5,1)$ are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line $y=2x+k$ , then the value of $k$ is

• A. 4
• B. 3
• C. -4
• D. -3
• E. 1

Answer 1

Answer: (C)

Now, mid-point of $A$ and $B$ is
$C\left(\frac{2+5}{2},\frac{5+1}{2}\right)\text{ or }C\left(\frac{7}{2},3\right)$

We know that, the diagonals of a rectangle bisect each other.
So, the mid-point $C\left(\frac{7}{2},3\right)$ lies on a given line.
$\therefore 3=2\times \frac{7}{2}+k$
$\Rightarrow 3=7+k$
$\Rightarrow k=-4$