The problem asks you to find the midpoint of a line segment shown on a coordinate grid. Here's how we can solve it step-by-step:

Step 1: Identify the coordinates of the endpoints.

From the image, it looks like the two endpoints of the segment are approximately:

• Endpoint 1: $(-3, 2)$
• Endpoint 2: $(2, 4)$

Step 2: Use the midpoint formula.

The formula for finding the midpoint $M$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Step 3: Plug in the coordinates.

$M = \left( \frac{-3 + 2}{2}, \frac{2 + 4}{2} \right)$

Simplifying:

$M = \left( \frac{-1}{2}, \frac{6}{2} \right)$

$M = \left( -\frac{1}{2}, 3 \right)$

Final Answer:

The midpoint of the segment is $\left( -\frac{1}{2}, 3 \right)$.

Would you like further explanation on any step?

Here are 5 related questions you might want to explore:

1. How would you find the midpoint if the coordinates were decimals or fractions?
2. How can the midpoint formula be applied in three-dimensional space?
3. How does the midpoint relate to the concept of bisecting a segment?
4. Can the midpoint formula be used in geometry to find the center of a circle given its diameter?
5. What is the significance of the midpoint in physics, especially in problems involving motion?

Tip: Always double-check the coordinates of endpoints from the graph, as a small mistake in identifying them can affect the final answer.