The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x=8, x=10, \mathrm{y}=11$ and $\mathrm{y}=12$ is

The rectangle boundaries are defined by $x=8$, $x=10$, $y=11$, and $y=12$. Its center lies at the intersection of the diagonals.

Applying the midpoint formula to opposite vertices $A=(8,11)$ and $C=(10,12)$ gives the intersection coordinates as $\left(\frac{8+10}{2}, \frac{11+12}{2}\right)$.

$x = \frac{18}{2} = 9$ and $y = \frac{23}{2}$, yielding the center $\left(9, \frac{23}{2}\right)$.

Comparing with the options, B matches the computed result.