TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 7: Coordinate Geometry
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
Coordinate geometry connects algebra and geometry by representing points with ordered pairs. Students use the distance formula, section formula and area formula to solve geometric problems algebraically.
🧭 Concept Journey
📌 Core Concepts
Distance between (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)²+(y₂−y₁)²]. The midpoint is ((x₁+x₂)/2,(y₁+y₂)/2).
💡 Worked Example
Distance between (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)²+(y₂−y₁)²]. The midpoint is ((x₁+x₂)/2,(y₁+y₂)/2).
⚠️ Common Errors
For A(2,3) and B(8,11), distance = √(36+64)=10 and midpoint=(5,7).
🧠 Concept-Based MCQs
- A school map places the library and laboratory at two coordinate points. Students calculate the distance and midpoint and interpret what the midpoint represents.
Answer Key: 1-A, 2-A, 3-B, 4-A.
📊 Case-Based / Competency
Do not interchange x and y coordinates. For distance, subtract corresponding coordinates first and square the differences.
- Draw or identify the mathematical model.
- Select the relevant theorem/formula.
- Solve with complete working.
- Interpret and verify the answer.
🔎 Extension Case
The midpoint of (2,4) and (6,8) is: A) (4,6) B) (8,12) C) (2,2) D) (6,4)|Distance formula comes from: A) Pythagoras theorem B) area theorem C) probability D) similarity only|The area of a triangle with collinear vertices is: A) 1 B) 0 C) 2 D) undefined|The section formula is used to find a point that: A) divides a line segment in a given ratio B) always lies at origin C) is always midpoint D) has no coordinates
🔥 HOTS & Board Challenge
- Explain why the chosen method works.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept to a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/context.
- Write a 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board challenge
🎯 One-Minute Revision
coordinate plane → distance → midpoint/section → area → geometric interpretation
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can choose the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
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Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.