The Coordinate Plane: Points You Can Name

Two number lines, one grid

You already know the number line: a straight line with integers marked off, negatives on the left, positives on the right. The coordinate plane is what you get when you cross two of these. The horizontal one is the x-axis; the vertical one is the y-axis. Where they cross is the origin, the point we label (0, 0).

Every point in the plane gets a name made of two numbers, an ordered pair written (x, y). The first number tells you how far right or left to go along the x-axis; the second tells you how far up or down along the y-axis. The order matters: (3, 1) and (1, 3) are different points.

Plotting a point, step by step

1. Start at the origin (0, 0) — your home base every single time.
2. Read the first number. If it is positive, move that many units right; if negative, move left.
3. Read the second number. If positive, move that many units up; if negative, move down.
4. Mark a dot. That dot is the point. Label it with its ordered pair so you can find it later.

Plot (-4, 3):
  start at origin (0, 0)
  first number is -4  ->  move 4 units LEFT
  second number is 3  ->  move 3 units UP
  dot sits 4 left and 3 up from center

Plot (2, -5):
  start at origin (0, 0)
  first number is 2   ->  move 2 units RIGHT
  second number is -5 ->  move 5 units DOWN

The four quadrants

The two axes cut the plane into four regions called quadrants, numbered I, II, III, IV counter-clockwise starting from the top right. The signs of the coordinates tell you instantly which quadrant a point lives in.

Quadrant I  : (+, +)   e.g. (3, 5)
Quadrant II : (-, +)   e.g. (-3, 5)
Quadrant III: (-, -)   e.g. (-3, -5)
Quadrant IV : (+, -)   e.g. (3, -5)

A point ON an axis is in NO quadrant:
  (0, 4) sits on the y-axis
  (-6, 0) sits on the x-axis