The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices are lie on the line $y=2 x+\mathrm{c}$ where c is the constant, then co-ordinates of other two vertices are

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

If the line $2 x+y=\mathrm{k}$ passes though the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ internally in the ratio $3: 2$ then, $(k+1):(k-1)=$

If the equation of the median through vertex $\mathrm{A}(3, \mathrm{k})$ of $\triangle \mathrm{ABC}$ with vertices $\mathrm{B}(2,1)$ and $\mathrm{C}(-4,5)$ is $x+4 y=\mathrm{p}$, then $\mathrm{k}=$ where p and k are constants