Coordinate plane reference
A reference for the coordinate plane: the four quadrants and the signs of their coordinates, plus the core formulas for distance, midpoint, and slope between two points.
The four quadrants
| Quadrant | x sign | y sign | Example point |
|---|---|---|---|
| I | + | + | (3, 2) |
| II | − | + | (−3, 2) |
| III | − | − | (−3, −2) |
| IV | + | − | (3, −2) |
Key formulas
| Quantity | Formula |
|---|---|
| Distance | √( (x₂−x₁)² + (y₂−y₁)² ) |
| Midpoint | ( (x₁+x₂)/2 , (y₁+y₂)/2 ) |
| Slope | (y₂−y₁) / (x₂−x₁) |
The coordinate plane is built from a horizontal x-axis and a vertical y-axis that cross at the origin, the point (0, 0). Every location is an ordered pair (x, y): x tells you how far across, y how far up or down. The axes split the plane into four quadrants, numbered counterclockwise from the top right.
Need the full formulas?
See the Distance Formula, Midpoint Formula, and Slope Formula.
Reading coordinates
A point is written as (x, y), the x-coordinate first. The x value is the horizontal position, positive to the right of the origin and negative to the left. The y value is the vertical position, positive above and negative below. So (3, negative 2) sits three units right and two units down, in the fourth quadrant.
The four quadrants
The axes divide the plane into four quadrants, numbered one to four counterclockwise starting from the upper right. Quadrant one has both coordinates positive; quadrant two has negative x and positive y; quadrant three has both negative; quadrant four has positive x and negative y. Knowing the signs tells you which quadrant a point lands in at a glance.
FAQ
What is the origin?
The point (0, 0) where the x-axis and y-axis cross, the reference point for all coordinates.
Which quadrant is the point (−3, 2) in?
Quadrant II, where x is negative and y is positive.
How are coordinates written?
As an ordered pair (x, y), with the horizontal x-coordinate first and the vertical y-coordinate second.