Coordinate Geometry & Circles

Straight lines

For points $A(x_1, y_1)$ and $B(x_2, y_2)$:

$$\text{gradient } m = \frac{y_2 - y_1}{x_2 - x_1}, \quad \text{midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ $$\text{length } AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

The equation of a line through $(x_1, y_1)$ with gradient $m$ is $y - y_1 = m(x - x_1)$.