If the point $M\left(h,k\right)$ lie on the line $2x+3y=5$ such that $\left|MA-MB\right|$ is maximum where $A\left(1,2\right)$ and $B\left(2,3\right),$ then the value of $\left(h+k\right)$ is

As, $\left|MA-MB\right|\le AB$
$\therefore {\left|MA-MB\right|}_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}=AB,$ which is possible when $M$ is the point of intersection of the line joining $A\left(1,2\right), B\left(2,3\right)$ and $2x+3y=5$.

Equation of the line joining $A \& B$ is $x-y+1=0$

Hence, the point of intersection is $h=\frac{2}{5}, k=\frac{7}{5}$

Hence, $h+k=\frac{9}{5}=1.8$