The Coordinate Plane
The coordinate plane is a grid formed by two number lines crossing at right angles. Every point has an address called an ordered pair.
The Axes and Origin
The x-axis is horizontal; the y-axis is vertical. They cross at the origin (0, 0). The plane is divided into 4 quadrants (I–IV, labelled counter-clockwise from top-right).
Plotting Points
An ordered pair (x, y) gives the location: move x units horizontally, then y units vertically from the origin.
Plot (3, −2): go 3 right, 2 down.
Plot (−4, 1): go 4 left, 1 up.
Reading Graphs
To read a point, trace horizontally to the x-axis to get x, then vertically to the y-axis to get y. Always write (x, y) — x first, y second.
Distance Between Points
For two points on the same horizontal or vertical line, distance = |difference of the changing coordinate|.
Distance from (2, 3) to (7, 3) = |7−2| = 5.
FAQ
Which quadrant is (−3, −5) in? Quadrant III — both negative.
Is (x, y) or (y, x) correct? Always (x, y) — x first.
Quick Quiz
Test what you just learned. Choose the best answer for each question.