Sheet № 206 · Foundation + Higher · AQA · Edexcel · OCR
Coordinates and Plotting –
Coordinates and plotting form the foundation of all graph work in GCSE Maths. Being confident with reading, plotting, and working with coordinates is essential for topics from straight-line graphs to transformations.
§Key definitions
Question:
Plot the points A(3, 2), B(-1, 4), and C(-2, -3) on a grid.
Answer:
A is in the first quadrant, B in the second quadrant, C in the third quadrant.
Q1 (Foundation):
Write down the coordinates of a point in the third quadrant.
Q2 (Foundation):
Find the midpoint of (6, 2) and (10, 8).
Q3 (Higher):
P is (-4, 6) and the midpoint of P and Q is (1, 2). Find Q.
§Formulas to memorise
Coordinates are written as (x, y) — x first (along), y second (up)
Midpoint of (x₁, y₁) and (x₂, y₂) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Worked example
Plot the points A(3, 2), B(-1, 4), and C(-2, -3) on a grid.
Working:
⚠ Common mistakes
- ✗Writing coordinates in the wrong order. The x value always comes first: (x, y), not (y, x). A helpful memory aid is "along the corridor before up the stairs."
- ✗Plotting negative values in the wrong direction. Negative x means go left; negative y means go down. Students sometimes go right for all x values.
- ✗Averaging incorrectly for midpoints. When one coordinate is negative, be careful with addition: (5 + (-3)) / 2 = 2 / 2 = 1, not 8/2 = 4.
✦ Exam tips
- →Always label your points with their letters on the graph — this is often required.
- →Use a small cross (x) to mark points, not a large dot — it is more precise.
- →For midpoint questions, if you are given the midpoint and one endpoint, work backwards by doubling the midpoint values and subtracting the known endpoint.