To find the midpoint of the line segment with endpoints $A(1, 3)$ and $B(5, 7)$, we use the midpoint formula:

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

Given:

• $A(1, 3)$ where $x_1 = 1$ and $y_1 = 3$,
• $B(5, 7)$ where $x_2 = 5$ and $y_2 = 7$,

Plugging the coordinates into the formula:

$M = \left( \frac{1 + 5}{2}, \frac{3 + 7}{2} \right)$

Simplifying:

$M = \left( \frac{6}{2}, \frac{10}{2} \right) = (3, 5)$

So, the midpoint is $(3, 5)$, which corresponds to option B.

Do you want more details or have any questions?

Here are 5 questions to expand this:

1. What is the general formula for finding the midpoint of two points?
2. Can the midpoint formula be applied in three-dimensional space? How?
3. How is the midpoint used in dividing line segments in geometry?
4. If the endpoints have negative coordinates, does the midpoint formula change?
5. How does the distance between two points relate to their midpoint?

Tip: When calculating midpoints, remember you're simply averaging the x and y coordinates of the two endpoints.