The Cartesian plane

Drawing the plane

Exams award a mark for each feature of a correctly drawn Cartesian plane, so make them a checklist:

• arrows on both ends of both axes
• axes labelled $x$ (horizontal) and $y$ (vertical)
• the origin marked O
• an evenly spaced number scale on each axis

The axes split the plane into four quadrants, numbered 1 to 4 going anticlockwise from the top right.

Plotting and reading points

Coordinates are written $(x, y)$: move across first, then up or down. Label each point with its letter as the question asks. If either coordinate is 0 the point sits on an axis: $(0, 4)$ is on the $y$-axis and $(-1, 0)$ is on the $x$-axis.

Before plotting anything, read the scale. A question asking you to plot $(0, 300)$ or $(2, -100)$ needs a scale counting in hundreds — one grid square is not always one unit.

Distances on the grid

If two points share a $y$-coordinate they sit on the same horizontal line, and the distance between them is the difference of the $x$-coordinates. Points sharing an $x$-coordinate work the same way vertically: from $(3, -2)$ up to $(3, 5)$ is $7$ units. Count the units or subtract — no formula needed at this level.

Shapes and reflections

A favourite exam question draws a shape in one quadrant and asks for the matching shape in the others. Reflections just flip signs:

• Reflecting in the $x$-axis changes the sign of $y$: $(2, 4) \to (2, -4)$.
• Reflecting in the $y$-axis changes the sign of $x$: $(2, 4) \to (-2, 4)$.
• The quadrant-3 copy changes both signs: $(2, 4) \to (-2, -4)$.

Write out the new ordered pairs before plotting, then join the points in the same order as the original shape.