Coordinates describe a position in 2D (or 3D) space using ordered pairs. In 2D, a coordinate is written as $(x, y)$ where $x$ is the horizontal position (along) and $y$ is the vertical position (up).
The four quadrants:
- Quadrant 1: $(+, +)$ — top right
- Quadrant 2: $(-, +)$ — top left
- Quadrant 3: $(-, -)$ — bottom left
- Quadrant 4: $(+, -)$ — bottom right
Plotting a point: start at the origin, move horizontally by $x$, then vertically by $y$.
3D coordinates: $(x, y, z)$ — add a third axis coming out of the page. Used in GCSE for locating vertices of 3D shapes.
Common uses: plotting graphs, describing transformations, finding midpoints, distances.
Distance between two points (using Pythagoras): $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
Common error: swapping $x$ and $y$ — remember "along the corridor, then up the stairs" ($x$ first, $y$ second).