Question

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

• A. $4$
• B. $3$
• C. $-4$
• D. $-3$

Answer 1

The correct option is C

$-4$

Compute the required value:

We know that the diagonals of a rectangle bisect each other.

So the midpoint of $(2,5)$ and $(5,1)$ will satisfy $y=2x+k$.

Midpoint $=\left(\frac{(2+5)}{2},\frac{(5+1)}{2}\right)$

$=\left(\frac{7}{2},3\right)$

$\left(\frac{7}{2},3\right)$ lies on $y=2x+k$

$\Rightarrow 3=2\times \frac{7}{2}+k$

$\Rightarrow k=3–7$

$\Rightarrow k=-4$

Hence option $\left(C\right)$ is the correct option.