Step 1: Understanding the Concept:
The given lines form a rectangle whose sides are parallel to the coordinate axes. A key property of any rectangle is that the intersection point of its diagonals is exactly its geometric center. For a rectangle aligned with the axes, this center is simply the midpoint of its horizontal and vertical boundaries.
Step 2: Key Formula or Approach:
The midpoint formula for a line segment between $(x_1, y_1)$ and $(x_2, y_2)$ is $M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
For an axis-aligned rectangle bounded by $x=x_1, x=x_2$ and $y=y_1, y=y_2$, the center is exactly $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
Step 3: Detailed Explanation:
The vertical boundaries of the rectangle are given by $x = 8$ and $x = 10$.
The horizontal boundaries of the rectangle are given by $y = 11$ and $y = 12$.
The x-coordinate of the center is the average of the x-boundaries:
\[ x_{\text{center}} = \frac{8 + 10}{2} = \frac{18}{2} = 9 \]
The y-coordinate of the center is the average of the y-boundaries:
\[ y_{\text{center}} = \frac{11 + 12}{2} = \frac{23}{2} \]
Therefore, the point of intersection of the diagonals is the center point $(9, \frac{23}{2})$.
Step 4: Final Answer:
The point of intersection is $\left(9, \frac{23}{2}\right)$.