# Geometry of the Plane

## Other Formulas

Distance. The formula for calculating the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.$$ Proof. We can prove this formula using the Pythagorean Theorem.
One can observe that the distance solves the equation: $${\rm distance}^2 = |x_1-x_2|^2 + |y_1-y_2|^2$$ so it takes the formula above.

Slope of a line segment. The formula for calculating the slope of a line segment between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_1-y_2}{x_1-x_2}.$$

Midpoint. The formula for calculating the midpoint between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$\left( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$