To find the midpoint of points $A(5, 3)$ and $B(9, -4)$ graphically, we will use the Midpoint Formula provided:

$\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Step-by-Step Solution:

1. Identify the coordinates:

   • $A(5, 3)$
   • $B(9, -4)$

2. Apply the Midpoint Formula: $x = \frac{5 + 9}{2} = \frac{14}{2} = 7$ $y = \frac{3 + (-4)}{2} = \frac{3 - 4}{2} = \frac{-1}{2} = -0.5$

   So, the midpoint is $(7, -0.5)$.

Graphical Interpretation:

• Plot points $A(5, 3)$ and $B(9, -4)$ on the graph.
• Then, plot the midpoint at $(7, -0.5)$.

If you'd like, I can assist further with drawing or verifying on the grid.

Would you like more details on the steps? Here are five related questions:

1. How can we verify the accuracy of a midpoint calculation?
2. What would happen to the midpoint if both points were mirrored?
3. How can the midpoint formula be extended to 3D coordinates?
4. How do midpoints relate to line segments in geometry?
5. Can the midpoint be used to find the slope of the line segment between two points?

Tip: The midpoint gives the average location of two points, which is useful in finding centers and bisecting lines.