How do you find the midpoint between two points in a coordinate plane?

To find the midpoint between two points in a coordinate plane, you take the average of the x-coordinates and the average of the y-coordinates of the two points. This method effectively locates the point that is exactly halfway between them.

If you have two points, say ( (x_1, y_1) ) and ( (x_2, y_2) ), the formula for the midpoint, ( M ), is given by [ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right). ] This calculation gives you a new point that represents the center along the straight line connecting the two original points.

Averaging the x-coordinates provides the x-coordinate of the midpoint, while averaging the y-coordinates gives the y-coordinate of the midpoint. This procedure is a fundamental geometry concept used frequently in coordinate systems.