Chapter 7 · Class X Mathematics · NCERT Exercises

Coordinate Geometry — Exercises

Distance · Section · Area — All Coordinate Geometry Problems Solved

📂 2 Exercises 📝 20 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 7.1

Distance formula; collinearity; type of quadrilateral/triangle

10 Q Easy-Moderate

②

Exercise 7.2

Section formula (internal & external); midpoint; trisection

10 Q hard

2 exercise files · 20 total questions

Chapter at a Glance

CBSE BoardsNTSEJEE Foundation

7 Concepts

6 Formulas

Moderate Difficulty

6–8% Weightage

Before You Begin

Prerequisites

✓Cartesian plane (Class IX)
✓Algebraic manipulation
✓Basic geometry — triangles and quadrilaterals

Have Ready

🔧Graph paper
🔧Ruler
🔧Distance formula reference card

Exercise Topic Map

Exercise 7.1 PQ = √[(x₂−x₁)²+(y₂−y₁)²]; for shape classification: compute all sides and diagonals

Exercise 7.2 P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)); midpoint when m=n=1

Key Formulae — Recall Before Solving

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(P = \!\left(\dfrac{mx_2+nx_1}{m+n},\, \dfrac{my_2+ny_1}{m+n}\right)\)

\(\text{Area} = \tfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\)

\(G = \!\left(\dfrac{x_1+x_2+x_3}{3},\,\dfrac{y_1+y_2+y_3}{3}\right)\)

NCERT Solving Method

Step 1 — Distance formula: expand carefully; no sign errors under the radical. Step 2 — Shape classification: equilateral △ → all sides equal; isosceles → two sides equal; rhombus → all sides equal + diagonals unequal; square → all sides equal + diagonals equal. Step 3 — Section formula: always label m:n ratio correctly; external division uses minus in numerator. Step 4 — Area = 0 confirms collinearity; never skip the absolute value.