Page 1: Introduction

Coordinate geometry links algebra and geometry using coordinates.

Tools: distance formula, section formula, area of triangle.

Used to find mid-points, centroids, collinearity, etc.

Page 2: Distance Formula

Derived from Pythagoras.

Page 3: Applications of Distance Formula

Verify equilateral, isosceles, right triangle.

Find length of sides.

Page 4: Section Formula - Internal Division

Mid-point when m:n = 1:1

Page 5: Section Formula - External Division

Page 6: Area of Triangle

If area = 0 → collinear points

Page 7: Collinearity of Points

Three points collinear if area = 0 or slope between pairs equal.

Page 8: Centroid of Triangle

Intersection of medians.

Page 9: Key Formulas Summary

• Distance formula
• Section internal/external
• Area of triangle
• Centroid

Page 10: Practice Questions - Easy (1-10)

1. Distance between (0,0) and (3,4).
2. Mid-point of (2,3) and (4,7).
3. Area of (0,0),(3,0),(0,4).
4. Section formula m:n = 2:3 example.
5. Collinear check area=0.
6. Centroid of (1,1),(2,2),(3,3).
7. External division 1:1.
8. Verify equilateral triangle.
9. Points on x-axis.
10. Distance from origin.

Page 11: Practice Questions - Medium (11-20)

11. Find k if points collinear.
12. Section formula 3:2 division.
13. Area of quadrilateral by splitting.
14. Centroid of given triangle.
15. Point dividing externally 2:1.
16. Verify isosceles using distance.
17. Find ratio if point divides internally.
18. Coordinates of point equidistant.
19. Area zero proof collinear.
20. Find missing coordinate.

Page 12: Practice Questions - Hard (21-30)

21. Points divide in ratio, find coordinates.
22. Centroid and section combined.
23. Prove collinear using slope/area.
24. Find ratio externally.
25. Area of polygon.
26. Board level collinear proof.
27. Find point dividing in given ratio.
28. Verify right triangle.
29. Multiple points problem.
30. Find coordinates using distance.

Page 13: Important Formulas Table

Distance, section, area, centroid.

Page 14: Common Mistakes

• Wrong sign in external section
• Forgetting absolute value in area
• Wrong ratio order
• Missing /3 in centroid
• Confusing internal/external

Page 15: Previous Year Questions

Section formula, area, collinear, centroid.

Page 16: Exam Tips

• Write formula first
• Show calculation steps
• Use absolute value for area
• Check collinear by area=0
• Memorise section formulas

Page 17: Quick Revision Sheet

All formulas, applications.

Page 18: Final Motivation

Chapter 7 complete! Coordinate Geometry is scoring.

Practice section and area numericals.

Class 10 Maths unstoppable 🦖

Page 19: Extra Numericals

More solved problems.

Page 20: Section Formula Derivation Hint

Weighted average.

Page 21: Area Formula Proof

Using vectors or determinant.

Page 22: Collinearity Methods

Area, slope, distance.

Page 23: Board Pattern Questions

Common types.

Page 24: Extra Practice

More questions.

Page 25: Applications

Centroid in physics, etc.

Page 26: Distance Special Cases

Horizontal, vertical lines.