To find the midpoint of the line segment connecting the points $(4, -3)$ and $(-6, 2)$, we use the midpoint formula:

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

Here, $(x_1, y_1) = (4, -3)$ and $(x_2, y_2) = (-6, 2)$.

Let’s calculate the midpoint step by step:

1. X-coordinate: $\frac{4 + (-6)}{2} = \frac{-2}{2} = -1$

2. Y-coordinate: $\frac{-3 + 2}{2} = \frac{-1}{2}$

Thus, the midpoint is $\left( -1, -\frac{1}{2} \right)$.

The correct answer is (e) $(-1, -\frac{1}{2})$.

Would you like further clarification or details on any part?

Here are 5 related questions you might find interesting:

1. How do you find the distance between two points?
2. What is the formula for the slope of a line through two points?
3. Can you determine the equation of the line connecting these two points?
4. How would the midpoint formula change in three dimensions?
5. What are some real-world applications of the midpoint formula?

Tip: The midpoint formula is the average of the x-coordinates and y-coordinates of two points, making it a key tool in geometry for bisecting line segments.