The Coordinate Plane & Plotting Points

Q: Which number comes first in an ordered pair?

The $x$-coordinate — the horizontal move — always comes first. A quick memory aid: $x$ comes before $y$ in the alphabet, and you move across before you move up or down.

Q: What if one of the coordinates is 0?

The point sits on an axis. If $y = 0$, it is on the $x$-axis; if $x = 0$, it is on the $y$-axis. The origin $(0, 0)$ is on both.

The coordinate plane is two number lines glued together: a horizontal one (the $x$ -axis) and a vertical one (the $y$ -axis). They cross at the origin, the point $(0, 0)$ . Every location on the plane gets a name — an ordered pair like $(3, -2)$ — and every ordered pair points to exactly one spot.

Reading and plotting ordered pairs is the on-ramp to everything that comes next: graphing lines, finding slope, and checking solutions. The whole skill comes down to one habit — the first number is the horizontal move, the second number is the vertical move, always in that order.

How to read an ordered pair

An ordered pair $(x, y)$ gives directions from the origin. The first number tells you how far to move right (positive) or left (negative). The second number tells you how far to move up (positive) or down (negative).

Take $(3, -2)$ . Start at the origin, move $3$ to the right, then $2$ down. That is the point shown on the graph below.

The four quadrants

The two axes split the plane into four regions called quadrants, numbered I, II, III, IV going counterclockwise from the top right.

You can name a point's quadrant from the signs alone. Quadrant I is $(+, +)$ , Quadrant II is $(-, +)$ , Quadrant III is $(-, -)$ , and Quadrant IV is $(+, -)$ . So $(-2, 5)$ — left and up — lands in Quadrant II without plotting anything.

Points on the axes

If a point sits on the $x$ -axis, its $y$ -coordinate is $0$ : points like $(4, 0)$ or $(-4, 0)$ . If it sits on the $y$ -axis, its $x$ -coordinate is $0$ : points like $(0, 3)$ .

Points on an axis are not in any quadrant — the quadrants are the four open regions between the axes. Whenever you see a $0$ in an ordered pair, expect the point to land on an axis.

Worked examples

Example 1: name the coordinates

A point sits $3$ units right of the origin and $2$ units down. Write its coordinates.

The horizontal move comes first:

3

right

x = 3

The vertical move comes second:

2

down

y = -2

Write the ordered pair

(3, -2)

Answer: $(3, -2)$

Example 2: plot a point

Plot the point $(-4, 2)$ .

Start at the origin

(0, 0)

The

x

-coordinate is negative, so move

4

left

The

y

-coordinate is positive, so move

2

Mark the point — it lands in Quadrant II

Answer: $(-4, 2)$ sits $4$ left and $2$ up from the origin

Example 3: name the quadrant

Which quadrant contains $(-5, -1)$ ?

The

x

-coordinate is negative, so the point is left of the

y

-axis

x = -5

The

y

-coordinate is negative, so the point is below the

x

-axis

y = -1

Left and down is the bottom-left region

\text{Quadrant III}

Answer: Quadrant III

Try one yourself

Common questions

Which number comes first in an ordered pair?

The $x$ -coordinate — the horizontal move — always comes first. A quick memory aid: $x$ comes before $y$ in the alphabet, and you move across before you move up or down.

(2, 5)

the same point as

(5, 2)

No. $(2, 5)$ means $2$ right and $5$ up; $(5, 2)$ means $5$ right and $2$ up. They are different locations — that is exactly why the pair is called ordered.

What if one of the coordinates is 0?

The point sits on an axis. If $y = 0$ , it is on the $x$ -axis; if $x = 0$ , it is on the $y$ -axis. The origin $(0, 0)$ is on both.

How do the quadrant numbers go?

Counterclockwise starting from the top right: Quadrant I is top right, II is top left, III is bottom left, IV is bottom right.

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The Coordinate Plane & Plotting Points

How to read an ordered pair

The four quadrants

Points on the axes

Worked examples

Example 1: name the coordinates

Example 2: plot a point

Example 3: name the quadrant

Try one yourself

Common questions

Keep learning

Graphing Linear Equations from a Table

Intro to Slope as Rate of Change

Solutions to Linear Equations

The Constant of Proportionality