Coordinate Geometry works with points and lines on the $x$–$y$ plane.
Key formulae
Gradient $= \dfrac{y_2 - y_1}{x_2 - x_1}$ · Midpoint $= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)$ · Distance $= \sqrt{(\Delta x)^2 + (\Delta y)^2}$
Example: the distance from $(0,0)$ to $(3,4)$ is $\sqrt{3^2+4^2} = 5$.
Remember
- Gradient = rise ÷ run.
- Midpoint = average of the coordinates.