What is the midpoint of the line segment with endpoints (3, 5) and (7, 9)?

The midpoint of the line segment with endpoints (3, 5) and (7, 9) is (5, 7).

To find the midpoint of a line segment, you use the midpoint formula, which is \((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\). This formula calculates the average of the x-coordinates and the y-coordinates of the endpoints. In this case, the endpoints are (3, 5) and (7, 9).

First, let's find the average of the x-coordinates. The x-coordinates are 3 and 7. Adding these together gives us \(3 + 7 = 10\). Then, we divide by 2 to find the average: \(\frac{10}{2} = 5\).

Next, we find the average of the y-coordinates. The y-coordinates are 5 and 9. Adding these together gives us \(5 + 9 = 14\). Then, we divide by 2 to find the average: \(\frac{14}{2} = 7\).

So, the midpoint of the line segment is \((5, 7)\). This point is exactly halfway between the two endpoints, both horizontally and vertically. Understanding how to find the midpoint is useful in various aspects of geometry and can help in solving problems related to bisecting lines and finding centres of shapes.