What you'll be able to do
- Name the parts of the coordinate plane: axes, origin, and quadrants.
- Write and read an ordered pair in the form (x, y).
- Plot and locate points in all four quadrants, including negatives.
Start with one number line
You've used a number line. It stretches out from 0 in two directions: positive numbers to the right, negative numbers to the left. Every number marks one exact spot.
. It stretches out from One number line is great for one piece of information, like temperature, or how many steps forward you took. But it can't tell you where something is on a flat surface, like a seat in a movie theater or a square on a map. For that, you need a second direction.
Cross two number lines
Take a horizontal number line and a vertical number line, and cross them so their zeros line up. Now you have a coordinate plane, a flat grid where every point has an address.
The two lines are called axes. The horizontal one is the x-axis. The vertical one is the y-axis. The spot where they cross—where both lines read zero—is the origin, written (0, 0).
The axes make four quadrants
The two axes split the plane into four corners called quadrants. They're numbered with Roman numerals I, II, III, IV, starting at the top-right and going counter-clockwise.
Which quadrant a point lands in depends only on the signs of its two numbers—whether each is positive or negative.
| Quadrant | x sign | y sign | Example |
|---|---|---|---|
| I | positive | positive | (4, 3) |
| II | negative | positive | (−4, 3) |
| III | negative | negative | (−4, −3) |
| IV | positive | negative | (4, −3) |
Try it
Number the quadrants yourself. Start with Quadrant I and click the quadrants in order.
Click the quadrant where I belongs.
Ordered pairs: (x, y)
A point's address is an ordered pair of two numbers, called its coordinates, written inside parentheses and separated by a comma.
The word ordered is the whole game: the order tells you which number does which job.
- The first number is the x-coordinate: how far to move across (right if positive, left if negative).
- The second number is the y-coordinate: how far to move up or down (up if positive, down if negative).
To plot a point, start at the origin, move across first, then up or down. Here's (3, 2): go right 3, then up 2.
Plotting in every quadrant
The rule never changes when numbers go negative. You just move the other way. A negative x means go left; a negative y means go down.
Look at (−4, 3): from the origin, go left 4, then up 3. That lands in Quadrant II.
Reading a point works in reverse. Find how far it sits across from the origin, then how far up or down. Write the across number first.
And watch for zeros: a point like (0, 4) has no across-movement, so it sits right on the y-axis. A point like (−3, 0) sits on the x-axis.
Quick checks
Try each one before you reveal the answer. These are just for you. No score is recorded.
Question 1
Which quadrant contains the point (−2, 5)?
Question 2
What is the ordered pair for point A?
Question 3
Where does the point (4, 0) sit?
Vocabulary
- Coordinate plane
- A flat grid formed by two number lines crossing at right angles.
- Axes
- The two number lines: the x-axis (horizontal) and the y-axis (vertical).
- Origin
- The point where the axes cross, with coordinates (0, 0).
- Ordered pair
- Two numbers (x, y) that give a point's address. Order matters.
- Coordinates
- The two numbers in an ordered pair: the x-coordinate (across) and the y-coordinate (up/down).
- Quadrant
- One of the four regions (I, II, III, IV) the axes divide the plane into.
Ready for the quiz?
Head to the Lesson 1 Quiz to plot points and identify quadrants. Work at your own pace. You can ask for a hint whenever you're stuck.
Go to Lesson 1 Quiz →