One of the diagonals of a square is the portion of the line $\frac{x}{2}+\frac{y}{3}=2$ intercepted between the axes. Then the extremities of the other diagonal are

The equation of the other diagonal is

 $\frac{x-2}{{\displaystyle \frac{3}{\sqrt{13}}}}=\frac{y-3}{{\displaystyle \frac{2}{\sqrt{13}}}}=r$

For the extremities of the diagonal, $r=\pm \sqrt{13}$. Hence $x-2=\pm 3,y-3=\pm 2$

x = 5, -1 and y = 5,1

Therefore, the extremities of the diagonal are (5,5) and (-1,1)