Maths Library

Cartesian coordinates: Year 9 maths

This topic covers plotting and reading points across all four quadrants on a Cartesian plane. The worksheet reinforces coordinate notation, midpoints of line segments, and geometric reasoning on grids.

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What this covers

Cartesian coordinates is taught in Year 9 (age 14 to 15) as a main teaching focus. It sits in the Algebra strand.

Worked example

Find the midpoint of the line segment joining A(2, -3) and B(6, 5).

  1. Calculate the x-coordinate of the midpoint: (2 + 6) ÷ 2 = 82 = 4
  2. Calculate the y-coordinate of the midpoint: (-3 + 5) ÷ 2 = 22 = 1
  3. Combine into coordinate pair notation: (4, 1)

Answer: (4, 1)

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Reading and plotting points in the first quadrant only
  2. Reading and plotting points across all four quadrants with integer values
  3. Finding missing vertices of simple shapes (rectangles, parallelograms) on a grid
  4. Calculating the midpoint between two coordinate points
  5. Finding an endpoint given one endpoint and the midpoint, or working with fractional coordinates

Common mistakes

  • Reversing the x and y coordinates, reading (y, x) instead of (x, y)
  • Moving in the wrong direction for negative coordinates, particularly on the vertical y-axis

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M9A04 Graph linear relations on the Cartesian plane, determining gradients and intercepts.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Cartesian coordinates

Year 9 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]
2.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]
3.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]
4.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]
5.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]
6.
Write down the coordinates of point A.
A-5-5-4-4-3-3-2-2-1-11122334455
[3]

Answer key

  1. (−1, −1)Go across first (x), then up or down (y); A is at (−1, −1)
  2. (2, 1)Go across first (x), then up or down (y); A is at (2, 1)
  3. (−5, 0)Go across first (x), then up or down (y); A is at (−5, 0)
  4. (−2, −4)Go across first (x), then up or down (y); A is at (−2, −4)
  5. (−5, 0)Go across first (x), then up or down (y); A is at (−5, 0)
  6. (−3, −5)Go across first (x), then up or down (y); A is at (−3, −5)