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Q.
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
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 $
$\Rightarrow k=-4$
