Skill: coordinate-plane

Coordinate Plane & Relations

Meet the coordinate plane: two number lines crossed at right angles, four quadrants, and one rule — x first, then y. Learn to plot any ordered pair, name any quadrant, and read relations as tables, graphs, and mappings.

1 Anatomy of the plane

The coordinate plane is a horizontal x-axis crossed with a vertical
y-axis at the origin (0, 0). The axes divide the plane into four
quadrants, numbered I, II, III, IV counterclockwise starting at the top right.

The one rule of plotting

(x, y): x first (left–right), then y (up–down)

Think “run before you jump”: walk along the x-axis first, then climb or drop along y.
(3, −2) is NOT (−2, 3) — order matters.

Plotting (3, −2): run 3 right along x, then drop 2 down along y — landing in Quadrant IV.

Sign patterns name the quadrant without plotting: Quadrant I (+, +), II (−, +),
III (−, −), IV (+, −). A zero coordinate means the point sits on an axis;
(0, 0) is the origin.

2 Worked examples

Plotting, naming, and measuring on the plane.

Example 1 Name the quadrant

Which quadrant contains (−4, 5)?

x is negative, y is positive: (−, +) is Quadrant II.

Example 2 On an axis

Where is (0, −3)?

x = 0, so the point sits on the y-axis — in no quadrant at all.

Example 3 Horizontal distance

Find the distance between (−2, 4) and (5, 4).

Same y, so just subtract the x’s: |5 − (−2)| = 7.

Example 4 Domain of a relation

Find the domain of {(1, 2), (3, 4), (5, 2)}.

The domain is the set of x-values: {1, 3, 5}.

3 Common mistakes

Three traps, each with the wrong version and the fix.

1. Swapping x and y

Wrong: plotting (3, −2) at (−2, 3).
Right: x first (left–right), then y (up–down) — “run before you jump”.

2. Calling the origin (1, 1)

Wrong: the origin is (1, 1).
Right: the origin is (0, 0) — where the axes cross.

3. Putting axis points in a quadrant

Wrong: (0, −3) is in Quadrant III.
Right: any zero coordinate means the point is on an axis, in no quadrant.

4 Quick checks

Try these yourself, then reveal the answer.

Which quadrant contains (6, −1)?

x positive, y negative: (+, −) is Quadrant IV.

Where is (−5, 0)?

y = 0, so it sits on the x-axis.

Find the range of {(2, 7), (4, 7), (6, 1)}.

The y-values: {7, 1} (list each once).

5 Key points

Remember

(x, y): x first (left–right), then y (up–down).
Quadrant signs: I (+,+), II (−+,), III (−,−), IV (+,−).
A zero coordinate puts the point on an axis; (0, 0) is the origin.
Distance along a horizontal or vertical segment is the absolute difference of the changing coordinate.
A relation is a set of ordered pairs; the domain is the x-values, the range the y-values.

Key vocabulary

Ordered pair

A point (x, y); order matters — (3, −2) differs from (−2, 3).

Quadrant

One of the four regions of the plane, numbered I–IV counterclockwise from the top right.

Origin

The point (0, 0) where the axes cross.

Relation

A set of ordered pairs, shown as a table, a graph, or a mapping diagram.

Domain

The set of all x-values (inputs) of a relation.

Range

The set of all y-values (outputs) of a relation.

Practice plotting
Open the point tool
Explore in the lab