Coordinates

#### Tier: #Foundation #Higher

Description

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).

Links

Equation of a straight line Pythagoras