Coordinates and the Number Plane

In short: A coordinate $(x,y)$ gives a point's position on a grid: go across by $x$ first, then up by $y$. The origin is $(0,0)$, and points to the left of it or below it have negative coordinates.

Before you start

• Negative numbers on a number line (see Negative and Positive Numbers).
• Horizontal means across, like the horizon. Vertical means up and down.

The number plane

The number plane has two number lines that cross at right angles:

• the $x$ axis goes across (horizontal)
• the $y$ axis goes up and down (vertical)
• they cross at the origin, the point $(0,0)$

Reading coordinates

In the diagram: $A=(3,2)$, $B=(-2,3)$, $C=(-4,-1)$ and $D=(1,-3)$.

The four quadrants

The axes split the plane into four quadrants, numbered anticlockwise from the top right.

A point that sits on an axis is not in any quadrant.

Distances along grid lines

If two points share the same $y$ value, they are on the same horizontal line. Their distance apart is the difference of their $x$ values.

Quick summary

• A point is written $(x,y)$: across first, then up.
• The origin is $(0,0)$. Left and down are negative.
• The quadrants go anticlockwise from top right: 1st $(+,+)$, 2nd $(-,+)$, 3rd $(-,-)$, 4th $(+,-)$.
• Points on an axis are not in a quadrant.
• Distance along a grid line is the difference of the changing coordinate.

Quiz