Coordinate Plane: All Quadrants

A coordinate plane is a flat grid built from two number lines that cross at right angles. The horizontal line is the x-axis, the vertical line is the y-axis, and the point where they meet is the origin, written as (0, 0). Together the two axes split the plane into four regions called quadrants.

The Four Quadrants

• Quadrant I — top right — both x and y are positive: (+, +).
• Quadrant II — top left — x is negative, y is positive: (-, +).
• Quadrant III — bottom left — both x and y are negative: (-, -).
• Quadrant IV — bottom right — x is positive, y is negative: (+, -).
• The quadrants are numbered counter-clockwise starting from the top right.

Reading and Plotting an Ordered Pair

1. An ordered pair is written (x, y) — x always comes first.
2. Start at the origin (0, 0).
3. Move along the x-axis: right if x is positive, left if x is negative.
4. Then move parallel to the y-axis: up if y is positive, down if y is negative.
5. Mark the spot with a dot and label it with its coordinates.

Worked Example: Plot (-3, 2)

1. x = -3, so move 3 units LEFT from the origin.
2. y = 2, so move 2 units UP from there.
3. The point lands in the top-left region — Quadrant II.
4. Sign check: x is negative and y is positive, which matches (-, +) for Quadrant II.

Points on the Axes

• A point with y = 0 sits ON the x-axis, not in any quadrant — for example (4, 0) or (-5, 0).
• A point with x = 0 sits ON the y-axis, not in any quadrant — for example (0, 3) or (0, -7).
• The origin (0, 0) is on BOTH axes and belongs to no quadrant.