CBSE Class 10 Maths Chapter 7 — Coordinate Geometry typically carries 6 marks (4–6%) in the board examination and is one of the highest-scoring chapters per hour of study. The chapter introduces three power-tools — Distance Formula, Section Formula and Area of Triangle — that recur in Chapter 8 (Trigonometry), Chapter 11 (Constructions), and Class 12 vectors. This NCERT-aligned guide covers all four exercises (7.1 to 7.4), every formula, two solved board-pattern problems, a chapter weightage table, and a 10-MCQ practice quiz at the end. Read it once, solve the quiz, and you have 6 marks locked.
Why Coordinate Geometry Matters in CBSE Class 10 Boards 2027
Looking at the last five years of CBSE 10 Maths board papers, Coordinate Geometry has produced at least one 3-mark and one 4-mark question every single year. The chapter is also the foundation for Class 11 Straight Lines and Class 12 Three-Dimensional Geometry. Our Class 10 chapter-wise resource hub tracks every PYQ since 2018.
Chapter 7 Weightage and Question Pattern (CBSE 2027)
| Topic / Sub-topic | Typical Marks | Question Type |
|---|---|---|
| Distance Formula | 1–2 | 1-mark MCQ + 2-mark short answer |
| Section Formula (internal & midpoint) | 2–3 | 2-mark / 3-mark |
| Area of Triangle (coordinates) | 3 | 3-mark short answer / collinearity |
| Word problem (real-life context) | 4 | 4-mark long-answer or case-study |
| Total Chapter 7 Weightage | 6 marks | ~7% of paper |
Master Formula Sheet
| Formula | Expression | Use |
|---|---|---|
| Distance Formula | d = sqrt((x2 – x1)^2 + (y2 – y1)^2) | Distance between any two points |
| Distance from Origin | d = sqrt(x^2 + y^2) | Special case when one point is (0,0) |
| Section Formula (internal, ratio m:n) | P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) | Point that divides AB in ratio m:n |
| Midpoint Formula | M = ((x1 + x2)/2, (y1 + y2)/2) | m = n = 1 special case |
| Centroid of Triangle | G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3) | Intersection of medians |
| Area of Triangle | A = 1/2 |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)| | Triangle from vertex coordinates |
| Collinearity Condition | Area of triangle = 0 | Three points lie on a straight line |
Exercise 7.1 — Distance Formula (NCERT Walkthrough)
Q1 (Sample). Find the distance between points (2, 3) and (4, 1).
d = sqrt((4-2)^2 + (1-3)^2) = sqrt(4 + 4) = sqrt(8) = 2.sqrt(2) units.
Q2 (Sample). Show that points (1, 5), (2, 3) and (-2, -11) are NOT collinear.
Distance AB = sqrt(1 + 4) = sqrt(5); BC = sqrt(16 + 196) = sqrt(212); AC = sqrt(9 + 256) = sqrt(265). Since AB + BC ≠ AC, points are not collinear.
Exercise 7.2 — Section Formula (Internal + Midpoint)
Q1 (Sample). Find the coordinates of the point which divides the line joining (–1, 7) and (4, –3) in the ratio 2:3.
P = ((2×4 + 3×(–1))/5, (2×(–3) + 3×7)/5) = ((8–3)/5, (–6+21)/5) = (1, 3).
Exercise 7.3 — Area of Triangle
Q1 (Sample). Find the area of the triangle formed by (1, –1), (–4, 6) and (–3, –5).
A = 1/2 |1(6 – (–5)) + (–4)((–5) – (–1)) + (–3)((–1) – 6)| = 1/2 |11 + 16 + 21| = 24 sq units.
Common Mistakes to Avoid
- Sign Errors in Section Formula: Mixing up x1 and x2 — write coordinates clearly above each variable.
- Missing the 1/2 factor: In area formula, students forget to multiply by 1/2.
- Modulus sign in area: Area is always positive; if expression is negative, take absolute value.
- External vs internal division: NCERT Chapter 7 covers only INTERNAL division — external is in higher classes.
- Distance formula squaring: Don’t forget to square individual differences before adding.
Real-Life Application Question (Board Pattern, 4-mark)
Q. A school is located at (3, 4) and a coaching centre at (–5, –2). A student lives exactly midway between them. Find the student’s coordinates and the distance she walks to school daily.
Solution. Midpoint M = ((3 + (–5))/2, (4 + (–2))/2) = (–1, 1). Distance from M to school = sqrt((3 – (–1))^2 + (4 – 1)^2) = sqrt(16 + 9) = sqrt(25) = 5 units. So the student walks 5 units (≈ 5 km if scale is in km) one way.
Quick Revision Mind Map
- Two points → Distance Formula → “Length needed?”
- Internal division → Section Formula → “Find the divider point?”
- Three points → Area of Triangle → “Are they collinear OR find area?”
- Three vertices → Centroid Formula → “Find G of triangle?”
Recommended Books and Reference Material
| Resource | Use | Time Required |
|---|---|---|
| NCERT Class 10 Maths (Chapter 7) | Primary text + every exercise | 4 hours |
| R.D. Sharma — Coordinate Geometry section | Extra practice problems | 3 hours |
| R.S. Aggarwal — for variety of word problems | Application questions | 2 hours |
| CBSE Sample Paper 2026-27 | Latest board pattern | 1 hour |
| Ready For Boards Coordinate Geometry PDF Notes | Quick revision sheet | 30 min |
Frequently Asked Questions
Q1. Can the section formula be derived?
Yes — using similar triangles. NCERT shows the derivation in section 7.3 of the textbook. Boards rarely ask the derivation, but it is recommended for conceptual clarity.
Q2. What if the three points form a triangle whose area comes negative?
Area cannot be negative — always take the absolute value. A negative result simply indicates the orientation (clockwise vs anticlockwise) of vertex listing.
Q3. Is the distance formula a special case of Pythagoras theorem?
Yes. The distance formula is essentially Pythagoras applied to a right-angled triangle whose horizontal side is (x2 – x1) and vertical side is (y2 – y1).
Q4. Are word problems on Coordinate Geometry common in CBSE Boards?
Yes — at least one 4-mark or 5-mark case-study problem appears in CBSE 10 Maths every year. Practice 5–10 such problems before exam.
Q5. How much time should I spend on Chapter 7?
10–12 hours is sufficient for mastery (4 hours theory + 4 hours NCERT exercises + 2 hours mock + 2 hours revision). Yields ~6 marks reliably.
Practice Quiz — 10 MCQs on Coordinate Geometry
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Next Steps for Class 10 Maths Mastery
Pair this chapter with NCERT Chapter 8 (Introduction to Trigonometry) for a related 8-mark cluster. Download our complete Class 10 Maths Formula Sheet PDF and join the Class 10 Maths Live Mentor Programme for daily problem-solving + weekly chapter tests + personal teacher access. Coordinate Geometry is among the easiest chapters to master — invest 12 hours and seal 6 marks for the boards.
