Coordinates in all four quadrants

Edexcel uses coordinates as the foundation for graphs, transformations and vector geometry. Reading them correctly across all four quadrants is non-negotiable; tested heavily on Paper 1F and underpins Higher work.

Quadrant naming

Quadrants are labelled anti-clockwise starting top-right:

• Quadrant I: x > 0, y > 0 (top right).
• Quadrant II: x < 0, y > 0 (top left).
• Quadrant III: x < 0, y < 0 (bottom left).
• Quadrant IV: x > 0, y < 0 (bottom right).

Reading and writing coordinates

A coordinate pair (x, y) gives horizontal first, vertical second. Common slip: reversing them — Edexcel always writes (4, −3) meaning 4 right and 3 down.

Midpoint of a line segment

Midpoint of A(x₁, y₁) and B(x₂, y₂) = ((x₁ + x₂)/2, (y₁ + y₂)/2).

Example: midpoint of (−4, 1) and (6, −5) = (1, −2).

Length of a line segment (distance formula)

|AB| = √((x₂ − x₁)² + (y₂ − y₁)²)

This is Pythagoras applied to the horizontal and vertical differences. Higher only — Foundation candidates use a square-grid count.

Coordinate transformations (linked to G8)

• Reflection in the x-axis: (x, y) → (x, −y).
• Reflection in the y-axis: (x, y) → (−x, y).
• 180° rotation about origin: (x, y) → (−x, −y).
• Translation by (a, b): (x, y) → (x + a, y + b).

Common Edexcel exam tip

If a question mentions a "midpoint", "centre" or "halfway point", the midpoint formula is almost always the correct first step. Show the working M1 + A1 — never just write the answer.