The formula you've written is the midpoint formula. It is used to find the point exactly halfway between two given points $(x_1, y_1)$ and $(x_2, y_2)$ on a coordinate plane.

The formula is:

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

Explanation:

• $x_1, y_1$ are the coordinates of the first point.
• $x_2, y_2$ are the coordinates of the second point.
• The midpoint is the average of the $x$-coordinates and the $y$-coordinates of the two points.

Example:

If the points are $(2, 3)$ and $(8, 7)$, the midpoint is:

$\text{Midpoint} = \left( \frac{2 + 8}{2}, \frac{3 + 7}{2} \right) = \left( \frac{10}{2}, \frac{10}{2} \right) = (5, 5)$

Would you like more details or have any questions?

Here are 5 relative questions for further understanding:

1. How do you find the midpoint if the coordinates include negative numbers?
2. What is the geometric significance of a midpoint in a line segment?
3. Can the midpoint formula be applied in three dimensions, and how?
4. How can you use the midpoint formula to find the center of a line segment in a triangle?
5. What is the relationship between the midpoint and the distance formula?

Tip: The midpoint formula works on any line segment, no matter how steep or flat the line is.