Coordinate geometry – Grade 10 math lesson
Lesson 14 of 16 in the Grade 10 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 10 (ages 15–16)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- 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.
- Finish with the exit ticket and the talk question: “How could you prove a shape is a square using only coordinates?”
- 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
Learning goal: 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 centered at (h, k) with radius r has equation (x − h)² + (y − k)² = r². Slopes show whether lines are parallel or perpendicular.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 10 math lessons
- Factoring
- Quadratic equations
- Identities and proof
- Functions
- Graphing functions
- Exponential functions
- Circles: circumference and area
- Volume and surface area
- The Pythagorean theorem
- Right triangle trigonometry
- Transformations
- Similarity and congruence
- Properties of quadrilaterals
- Cross sections of 3-D figures
- Geometric constructions
Curriculum
Common Core State Standards HSG.GPE.A.1: “Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.”
Common Core State Standards HSG.GPE.B.4: “Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.