Distance Formula

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a Cartesian plane is given by the Pythagorean theorem.

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Midpoint Formula

The midpoint $M$ of the line segment connecting the two points is the average of their coordinates.

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