The Coordinate Plane

The coordinate plane uses two perpendicular number lines (axes) to locate any point using an ordered pair (x, y). It is divided into four quadrants.

The Axes

The x-axis runs horizontally. The y-axis runs vertically. They meet at the origin (0, 0).

The coordinate plane with all four quadrants and example points labeled.

Ordered Pairs

A point is written as $(x, y)$ — the x-coordinate first, then the y-coordinate.

$x > 0$ : right of origin
$x < 0$ : left of origin
$y > 0$ : above origin
$y < 0$ : below origin

Tip Remember: "x comes before y" — move horizontally first, then vertically.

The Four Quadrants

Quadrant	x	y	Example
I (top-right)	+	+	(3, 5)
II (top-left)	−	+	(−2, 4)
III (bottom-left)	−	−	(−3, −1)
IV (bottom-right)	+	−	(4, −2)

Plotting Points

1
Start at the origin (0, 0)
The centre of the grid.
2
Move horizontally by the x value
Right if positive, left if negative.
3
Move vertically by the y value
Up if positive, down if negative.
4
Mark the point
Draw a dot and label it.

Distance Between Points on an Axis

If two points share the same y-value, their distance = $|x_2 - x_1|$ .

If they share the same x-value, distance = $|y_2 - y_1|$ .

Plot A(−2, 3) and B(4, 3). Find the distance AB.

Both have $y = 3$ , so they lie on a horizontal line.

$AB = |4 - (-2)| = 6 \text{ units}$

Real world: GPS and maps

Every location on Earth is described by two coordinates — latitude and longitude — just like $(x, y)$ on the coordinate plane. London is roughly at (51.5, −0.1): 51.5° north, 0.1° west.

Real world: video-game character position

A game character stands at position (3, 7) on a 2D grid. Moving 4 units right and 2 units up places the character at $(3+4,\; 7+2) = (7, 9)$ . The coordinate system tracks every move.

Real world: seat numbering in a cinema

A cinema seat labelled Row F, Seat 12 is essentially coordinates (12, 6) — column first, row second. The same ordered-pair logic helps you find any seat quickly.

Practice Problems

In which quadrant does (−5, 2) lie?

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Quadrant II (x negative, y positive).

What are the coordinates of the origin?

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(0, 0).