Coordinate Geometry Worksheets

What this worksheet covers

A coordinate geometry handout is a printable run of grid and axis items, and the marking key can ride along or stay back. Nothing comes from a stored bank: each item is drawn fresh when the sheet is built, which is why two handouts at one rung differ.

Items on the sheet look like this:

• find the midpoint of (4, 2) and (10, 8)
• find the gradient through (2, 3) and (6, 11)
• find the distance from (0, 0) to (6, 8)
• write the equation of the line of gradient 4 through (0, −2)
• write the equation of the line through (1, 6) and (3, 14)
• decide whether y = 2x + 5 and y = 2x − 3 are parallel
• plot the points and join them

Choosing a level

The early rungs move from reading plotted locations to calculating with pairs. Warm-Up asks for a grid reading; Basics averages two coordinate pairs. Steady builds a line equation from given points, and Mastery compares equations to decide whether their lines are parallel. The picker labels the range from easiest to hardest.

Set the printout to any whole count from 3 to 15. Keep every task at the chosen difficulty, or switch to Mixed difficulties to revisit the other rungs from that starting point.

Write-in leaves the coordinate differences visible, so the marker can check their order. A–D can check a learner's choice of rise over run quickly, though it hides the subtraction behind the selected answer.

A worked example

The key can show each coordinate difference explicitly, so the order of subtraction is easy to inspect.

Find the gradient through (2, 3) and (6, 11). Subtract in the same order both times: (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2. The y-difference is 8 and the x-difference is 4, so the line climbs 2 for every 1 across.

Find the equation of the line through (1, 6) and (3, 14). The gradient is (14 − 6) ÷ (3 − 1) = 4. Substituting (1, 6) into y = 4x + c gives 6 = 4 + c, so c = 2 and the line is y = 4x + 2.

Marking with the answer key

Many marking errors come from reversing a subtraction or swapping the rise and run.

• The midpoint answered (14, 10). The two coordinates were added and left there. A midpoint sits halfway, so each pair is averaged: (4 + 10) ÷ 2 and (2 + 8) ÷ 2 give (7, 5).
• The gradient answered 0.5. The x-difference went over the y-difference. Rise over run means (11 − 3) ÷ (6 − 2) = 2.
• The distance answered 14. That is 6 + 8, the two steps added instead of squared. The steps are the legs of a right triangle, so 36 + 64 = 100 and the distance is 10.
• The line through (0, −2) with gradient 4 answered y = 4x + 2. The intercept lost its sign. The point (0, −2) gives c = −2, so the line is y = 4x − 2.

Printing and using it

Keep a clear grid beside the plotting tasks. Print on squared paper or at full size; shrinking the page makes coordinate points harder to place accurately.

Standard leaves room beneath each task for coordinate subtraction. Large-print separates the brackets and signs for learners still getting used to ordered pairs. Compact fits twelve short readings on one side for a starter.

Add a Name / Date / Class header when collecting the pages. Dyslexia-friendly type can separate a negative coordinate from the brackets around its point. Stretch raises each third task one level, provided the sheet uses a single difficulty. A title such as "Gradient from two points" names the skill being practised.

For a partner check, one learner reads an ordered pair and the other plots it. Swap roles and compare both points with the key before finding the gradient or distance. Ask each partner to say aloud which value is x and which is y before placing the point.

Keep going

Take the same work onto the coordinate geometry practice ladder; marking happens there instantly. Read the coordinate geometry lesson for the midpoint and gradient rules side by side, or print functions worksheets, which cover the rule itself rather than its graph.

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