Algebra · Lesson 12 of 16

Coordinates in Four Quadrants

Coordinates (x, y) describe a position from the origin: x says how far across and y says how far up or down.

Secondary
Updated 14 November 2026

What you will learn

Plot and read points in all four quadrants.
Find distances and midpoints.
Complete a shape from its vertices.

Before you start: you should know negative numbers and how to plot points in the first quadrant. See Position, Direction and Turns.

The idea

Two number lines cross at right angles. The horizontal one is the x-axis and the vertical one is the y-axis. They meet at the origin, $(0, 0)$ . A point is written $(x, y)$ : go across first, then up or down.

Four points, one in each quadrant. A is in the first, B the second, C the third and D the fourth.

The four quadrants

The signs of the coordinates tell you the quadrant. Quadrants are numbered anticlockwise from the top right.

Distance and midpoint

If two points share a $y$ -coordinate, the distance is the difference in $x$ . The midpoint is the average of the coordinates.

M (4, 7) is the midpoint of P (2, 4) and Q (6, 10). Add the x values and halve, then add the y values and halve.

Worked examples

Example 1: Naming a quadrant

Which quadrant has the point $(-3, -4)$ ?

Both signs are negative.

Answer: the third quadrant

Example 2: Distance

Find the distance from $(-2, 3)$ to $(4, 3)$ .

Same $y$ , so subtract $x$ values.
$4 - (-2) = 6$ .

Answer: $6$

Example 3: Midpoint

Find the midpoint of $(2, 4)$ and $(6, 10)$ .

$x$ : $(2 + 6) \div 2 = 4$ .
$y$ : $(4 + 10) \div 2 = 7$ .

Answer: $(4, 7)$

Tip: say “along the corridor, then up the stairs” to remember x before y.

Why it matters

Coordinates are used in maps, games, screens and graphs. Next, linear equations draw straight lines on a coordinate grid.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.