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.

What Are Coordinates?

A coordinate is a pair of numbers written as (x, y) that describes the exact position of a point on a grid. The first number gives the horizontal position (along the x-axis) and the second gives the vertical position (up the y-axis). The point where the axes cross is called the origin, written as (0, 0).

The axes divide the grid into four quadrants. In the first quadrant (top right), both x and y are positive. In the second quadrant (top left), x is negative and y is positive. In the third quadrant (bottom left), both are negative. In the fourth quadrant (bottom right), x is positive and y is negative.

A common skill is finding the midpoint of two points. The midpoint is the point exactly halfway between them, found by averaging the x-coordinates and averaging the y-coordinates separately.

Key Formulas

Step-by-Step Method

1. To read coordinates, start at the point and read across to the x-axis for the x value, then up/down to the y-axis for the y value.
2. To plot a point, start at the origin, move along the x-axis by the x value, then up or down by the y value. Mark with a cross.
3. Remember: along the corridor (x) first, then up the stairs (y).
4. To find the midpoint, add the two x values and divide by 2, then add the two y values and divide by 2.
5. Write your answer as a coordinate pair in brackets.

Worked Example 1 — Foundation Level

Question: Plot the points A(3, 2), B(-1, 4), and C(-2, -3) on a grid.

Working:

Step 1 — Point A: move 3 right along the x-axis, then 2 up. Mark A.

Step 2 — Point B: move 1 left along the x-axis (negative x), then 4 up. Mark B.

Step 3 — Point C: move 2 left, then 3 down (negative y). Mark C.

Answer: A is in the first quadrant, B in the second quadrant, C in the third quadrant.

Worked Example 2 — Higher Level

Question: Find the midpoint of (4, 7) and (-2, 3).

Working:

Step 1 — Average the x-coordinates: (4 + (-2)) / 2 = 2 / 2 = 1.

Step 2 — Average the y-coordinates: (7 + 3) / 2 = 10 / 2 = 5.

Answer: Midpoint = (1, 5)

Worked Example 3 — Exam Style

Question: M is the midpoint of A(2, 5) and B(8, y). M has coordinates (5, 3). Find the value of y. (2 marks)

Working:

Step 1 — Check x: (2 + 8) / 2 = 10 / 2 = 5. This matches the x-coordinate of M. Correct.

Step 2 — Use the y-coordinate: (5 + y) / 2 = 3.

Step 3 — Multiply both sides by 2: 5 + y = 6.

Step 4 — Subtract 5: y = 1.

Answer: y = 1

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.

Practice Questions

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.

Practise coordinates and plotting questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Plotting Straight Line Graphs
• Linear Graphs and Equation of a Line
• Transformations: Reflection, Rotation, Translation

Summary

• Coordinates are written as (x, y): x is horizontal, y is vertical.
• The four quadrants are defined by the signs of x and y.
• To find the midpoint, average the x values and average the y values separately.
• Always write x before y and label plotted points clearly.
• Use a cross for accuracy when plotting on graph paper.