What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is \((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\).

To find the midpoint of a line segment, you need the coordinates of the two endpoints of the segment. Let's say the endpoints are \((x_1, y_1)\) and \((x_2, y_2)\). The midpoint is simply the average of the x-coordinates and the average of the y-coordinates of these endpoints. This means you add the x-coordinates together and divide by 2, and do the same for the y-coordinates.

For example, if you have a line segment with endpoints at \((2, 3)\) and \((4, 7)\), you can find the midpoint by calculating:
\[ x_{\text{mid}} = \frac{2 + 4}{2} = 3 \]
\[ y_{\text{mid}} = \frac{3 + 7}{2} = 5 \]
So, the midpoint of the line segment is \((3, 5)\).

This formula is very useful in various geometric problems, such as finding the centre of a line segment or dividing a line segment into equal parts. It’s also a fundamental concept in coordinate geometry, which you’ll encounter frequently in GCSE Maths. Remember, the midpoint is always equidistant from both endpoints, making it a perfect centre point of the line segment.