Orienting Yourself: The Use of Coordinates

Coordinates are a pair of numbers that tell the exact position of a point on a plane. The first number is the x-coordinate (horizontal distance from the origin) and the second is the y-coordinate (vertical distance). Together they are written as an ordered pair (x, y).

Start at the origin (0, 0). Move horizontally along the x-axis by the value of the x-coordinate, then move vertically by the value of the y-coordinate. The point where you stop is the location of the ordered pair (x, y).

The two axes divide the plane into four quadrants numbered anticlockwise. In Quadrant I both coordinates are positive (+, +), in Quadrant II x is negative and y positive (−, +), in Quadrant III both are negative (−, −), and in Quadrant IV x is positive and y negative (+, −).

The abscissa is the x-coordinate of a point, measuring its horizontal distance from the y-axis. The ordinate is the y-coordinate, measuring its vertical distance from the x-axis. In the pair (x, y), x is the abscissa and y is the ordinate.

Coordinate geometry lets us describe positions and shapes using numbers instead of pictures alone. It connects algebra and geometry, making it possible to graph equations, find distances, and study how two quantities change together — skills used throughout higher mathematics.

The origin is the point where the x-axis and y-axis cross. Its coordinates are (0, 0) because it is zero units from both axes. Every other point's position is measured relative to the origin.