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Coordinate geometry – Year 9 maths lesson

Lesson 18 of 38 in the Year 9 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.

Time
45 minutes + 20 min homework
Year
Year 9 (ages 13–14)
You need
Paper, a pencil and this page
Marked
Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.

  1. Read what your child will learn and the big ideas together.
  2. Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
  3. Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
  4. Finish with the exit ticket and the talk question: “How could you prove a shape is a square using only coordinates?”
  5. Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

  • Subtracting coordinates for the midpoint. Add and halve: it is an average.
  • Forgetting to square root for the distance. Pythagoras: square, add, then square root.

Tip for home: Use a map grid to work out straight-line distances.

What your child will learn

We are learning to use coordinates to find midpoints, lengths and equations of lines and circles.

Success looks like

  • I can find a midpoint.
  • I can find the distance between two points.
  • I can use equations of lines and circles.

Key words

midpoint
the point exactly halfway
distance
the straight-line length between two points
coordinates
a pair (x, y) giving a position
equation of a circle
a rule that every point on the circle fits

What to have ready

  • Paper and a pencil
  • This page on a computer, tablet or phone
  • For the hands-on part: Plot a shape on a grid and use coordinates to prove it is a rectangle or a kite.

The big ideas (for the adult)

The midpoint of two points is found by averaging the x-coordinates and averaging the y-coordinates.

The distance between two points comes from Pythagoras: √((x₂ − x₁)² + (y₂ − y₁)²).

A circle centred at (a, b) with radius r has equation (x − a)² + (y − b)² = r². Gradients show whether lines are parallel or perpendicular.

The lesson, step by step

45 minutes in 5 parts
PartTimeHow it is checked
Starter: quick recall5 minMarked by Classfern
Teaching input10 minNot assessed, self-checked
Worked examples and guided practice9 minNot assessed, marked by Classfern
Independent practice15 minMarked by Classfern
Plenary and exit ticket6 minMarked by Classfern, self-checked

Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.

More practice

All Year 9 maths lessons and tests · Maths Department

More Year 9 maths lessons

Curriculum

GCSE subject content G11: “solve geometrical problems on coordinate axes”

Contains public sector information licensed under the Open Government Licence v3.0.

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.