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Coordinates

FoundationAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on coordinates helps you revise plotting and reading coordinates. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Coordinates are written (x, y) — along the corridor, then up the stairs.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Topic overview

Coordinates locate a point on a grid using a pair of numbers. The first number is the \(x\) coordinate, giving the horizontal position, and the second is the \(y\) coordinate, giving the vertical position.

The order matters and is always the same: across first, then up. The point \((3, 5)\) is three across and five up, which is a completely different place from \((5, 3)\).

The axes divide the grid into four quadrants, and coordinates can be negative. A negative \(x\) means left of the origin and a negative \(y\) means below it, so \((-2, -4)\) sits in the bottom-left quadrant.

Revision notes

Reading and plotting

Start at the origin \((0, 0)\). Move along the \(x\)-axis first, then up or down parallel to the \(y\)-axis.

A useful reminder is along the corridor, up the stairs. Mark the point clearly with a cross or a dot and label it if the question asks.

Negative coordinates

The axes extend in both directions. Negative \(x\) values lie to the left, negative \(y\) values below.

So \((-3, 2)\) is three left and two up, while \((4, -1)\) is four right and one down.

Midpoints and simple distances

The midpoint of two points is found by averaging the coordinates separately.

For \((2, 3)\) and \((8, 7)\), the midpoint is \(\left(\frac{2+8}{2}, \frac{3+7}{2}\right) = (5, 5)\).

Key points

  • Coordinates are written as \((x, y)\).
  • The x coordinate comes first and is horizontal.
  • The y coordinate comes second and is vertical.
  • The origin is \((0, 0)\).
  • Negative x is left; negative y is down.
  • Average the coordinates to find a midpoint.

Worked examples

Example 1

Write down the coordinates of a point \(4\) right and \(3\) up from the origin.

Working

\[x = 4\]the horizontal distance comes first
\[(4, 3)\]write the pair with y second

Example 2

Plot the point \((-2, 5)\). Describe where it lies.

Working

\[\text{2 units left of the origin}\]a negative x means move left
\[\text{5 units up}\]a positive y means move up
\[\text{Top-left quadrant}\]state the region

Example 3

Find the midpoint of \((1, 4)\) and \((7, 10)\).

Working

\[\frac{1 + 7}{2} = 4\]average the x coordinates
\[\frac{4 + 10}{2} = 7\]average the y coordinates
\[(4, 7)\]write the midpoint as a coordinate pair

Common mistakes

  • Writing the coordinates the wrong way round.

    (3, 5) and (5, 3) are different points. Always x first.

  • Miscounting from the origin.

    Count the grid lines, not the squares between them.

  • Getting negative directions confused.

    Negative x is left and negative y is down, not the reverse.

  • Adding coordinates instead of averaging for a midpoint.

    The midpoint needs the mean of each pair, so divide by 2.

Exam tips

  • Say along the corridor, up the stairs to keep the order right.
  • Label plotted points clearly.
  • Count grid lines carefully when the scale is not 1.
  • Check which quadrant your answer should be in as a sense-check.

Key terms

Coordinate
A pair of numbers locating a point on a grid.
Origin
The point \((0, 0)\) where the axes cross.
Quadrant
One of the four regions the axes divide the grid into.
Midpoint
The point exactly halfway between two others.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.