The Cartesian Plane

The Cartesian plane is a grid made by two number lines crossing at right angles. The horizontal line is the $x$-axis, the vertical line is the $y$-axis, and they meet at the origin $(0, 0)$.

Every point has an address written as an ordered pair $(x, y)$: the first number is how far across (right is positive, left negative), the second is how far up (up positive, down negative). Order matters — $(3, -2)$ is not the same point as $(-2, 3)$.

The two axes split the plane into four quadrants, numbered anticlockwise from the top right: I $(+, +)$, II $(-, +)$, III $(-, -)$, IV $(+, -)$.

Worked example. Where is $(-4, 1)$? Go 4 left and 1 up — that puts the point in the second quadrant.