CBSE · Class 10 · Mathematics · Chapter 7
Coordinate Geometry — Class 10 Mathematics (CBSE) explained
- Board exam 2026-27
- 3 lessons
- 30 scenes
- About 21 min
- Updated
Quick answer
Coordinate Geometry is Chapter 7 of CBSE Class 10 Mathematics. It covers axis and diagonal distances, distance across quadrants, distance formula remarks and internal division in context. AI Lessons teaches it in 3 narrated lessons (about 21 minutes) with an AI tutor and board-pattern practice.
What you’ll learn
Lesson 1: From Coordinates to the Distance Formula
7 min- Coordinates Connect Algebra and Geometry
- Construct a Picture from Ordered Pairs
- Distances Along Axes and Across a Right Triangle
- Build a Right Triangle Between P and Q
- Distance Across Different Quadrants
- Derive the Distance Formula
- Origin Distance and Reversing Point Order
- Example One: Identify a Right Triangle
- Example Two: Calculate the Four Sides
- Example Two: Complete the Square Proof
Lesson 2: Distance Applications and Internal Division
7 min- Example Three: Are the Students Seated in a Line?
- Example Four: An Equation for Equal Distances
- Example Five: Find and Check the Y-Axis Point
- Exercise Seven Point One: Choose the Right Distance Test
- Locate a Relay Tower Between Two Towns
- Build the General Section-Formula Construction
- Derive the Internal Section Formula
- Write the Section Formula for K to One
- The Midpoint Formula Is a Special Case
- Example Six: Find the Internal Division Point
Lesson 3: Section Formula Applications and Practice
7 min- Example Seven: Find an Unknown Dividing Ratio
- Example Seven: Verify and Use the Alternative Method
- Example Eight: Find the Points of Trisection
- Example Nine: Where Does the Segment Meet the Y-Axis?
- Example Ten: Find the Missing Parallelogram Coordinate
- Exercise Seven Point Two: Ratios and the Sports Ground
- Exercise Seven Point Two: Shapes and Equal Parts
- Summary: Four Formulas, Different Questions
- Optional Enrichment: Recognise External DivisionNot assessed
- Recap: Interpret, Calculate, Justify and Practise
Key concepts
- Axis and diagonal distances
- The direct distance is a diagonal, not the sum of these two movements.
- Distance across quadrants
- The points lie in different quadrants, but the method stays the same.
- Distance formula remarks
- One subtracts the first point's coordinates from the second point's coordinates.
- Internal division in context
- Replacing those sides by coordinate lengths gives the two equations.
Exam focus
- Board exam
- CBSE assesses this chapter in the 2026-27 year-end board examination.
- Syllabus
- COORDINATE GEOMETRY: 1. Review: Concepts of coordinate geometry. Distance formula. Section formula (internal division). Competency: derives formulae to establish relations for geometrical shapes in the context of a coordinate plane, such as finding the distance between two given points, to determine the coordinates of a point between any two given points. Learning outcome: solves problems using distance formula and section formula.
- Not assessed
- These parts go beyond the 2026-27 syllabus and are taught for understanding only: Optional Enrichment: Recognise External Division.
- Exam note
- Section formula is for internal division only; external division is outside the syllabus.
- Exam note
- Area of a triangle from coordinates is not in the syllabus (and not in the 2026-27 textbook).
- Paper pattern
- Mathematics Standard: 80 marks, 3 hours, 38 questions. Section A: 18 MCQs + 2 assertion-reason (1 mark each); B: 5 VSA (2 marks); C: 6 SA (3 marks); D: 4 LA (5 marks); E: 3 case-study questions (4 marks). No calculators.
- Question style
- About 50% of board questions are competency-focused.
- Practice in the app
- 98 board-pattern questions with marking schemes: 28 multiple choice (1 mark), 11 assertion–reason (1 mark), 22 very short answer (2 marks), 24 short answer (3 marks), 5 long answer (5 marks) and 8 case-based (4 marks).
Sample questions with marking points
Board-pattern questions from the AI Lessons practice set for this chapter. The marking points show what an examiner looks for; full model answers are in the app.
Very short answer2 marks
P has abscissa a and ordinate b, while Q has abscissa -a and ordinate -b. Show that PQ is twice the distance of P from the origin O.
Marking points
- States OP = √(a² + b²).0.5
- Correctly substitutes the corresponding differences for PQ.0.5
- Obtains PQ = √(4a² + 4b²).0.5
- Simplifies and concludes PQ = 2OP.0.5
Short answer3 marks
A has abscissa 5 and ordinate -6; B has abscissa -1 and ordinate -4. A student claims that the y-axis bisects AB. Test the claim by finding the actual dividing ratio and the ordinate of the intersection.
Marking points
- Uses zero abscissa to form (-k + 5)/(k + 1) = 0.1
- Obtains k = 5 and AP : PB = 5 : 1, rejecting bisection.1
- Obtains ordinate -13/3.1
Frequently asked questions
What does Coordinate Geometry cover in Class 10 Mathematics?
It covers axis and diagonal distances, distance across quadrants, distance formula remarks and internal division in context. AI Lessons teaches it in 3 lessons: From Coordinates to the Distance Formula, Distance Applications and Internal Division and Section Formula Applications and Practice.
Is Coordinate Geometry in the CBSE Class 10 board exam?
Yes. CBSE assesses Coordinate Geometry in the 2026-27 year-end board examination. 1 short part goes beyond the syllabus and is marked as not assessed.
Which condition describes a point on the y-axis other than the origin?
Its abscissa is zero and its ordinate is nonzero. Every point on the y-axis has abscissa zero.
Which condition identifies a point on the x-axis other than the origin?
Its ordinate is zero and its abscissa is nonzero. A point on the x-axis has ordinate zero, and excluding the origin makes its abscissa nonzero.
What is the direct distance?
The direct distance is a diagonal, not the sum of these two movements.
What kinds of questions come from Coordinate Geometry?
Board-pattern questions for this chapter include multiple choice (1 mark), assertion–reason (1 mark), very short answer (2 marks), short answer (3 marks), long answer (5 marks) and case-based (4 marks). AI Lessons has 98 of them for Coordinate Geometry, each with a marking scheme.
How does AI Lessons teach Coordinate Geometry?
As 3 narrated, animated lessons (30 scenes, about 21 minutes in all), with an AI tutor that knows the step you are on and board-pattern practice with marking schemes. The full lessons open after sign-in on an AI Lessons account.
Watch the full lesson
Coordinate Geometry, as a narrated, animated lesson
3 lessons · 30 animated scenes · about 21 minutes, with an AI tutor that knows the step you are on and 98 board-pattern questions with marking schemes.
Lessons open after sign-in. A parent or guardian holds the account and adds each child.