Distance formula and section formula: Class 10 practice
Distance between (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²]. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Pythagoras theorem
- Ratios
The idea behind distance formula and section formula
Distance between (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²]. A point dividing the join in ratio m : n is ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).
Step-by-step method
- Label the points carefully.
- Distance: square the differences, add, take root.
- Section: weight each coordinate by the OPPOSITE ratio part.
Worked example 1 (Basic)
Find the distance between A(1, -4) and B(7, 4).
- Δx = 6, Δy = 8
- AB = √(36 + 64) = √100
- AB = 10 units
- Answer: 10 units
Worked example 2 (Standard)
Find the distance between A(-3, 1) and B(-8, 13).
- Δx = -5, Δy = 12
- AB = √(25 + 144) = √169
- AB = 13 units
- Answer: 13 units
Worked example 3 (Challenge)
Find the point dividing A(6, 5) and B(12, 2) internally in the ratio 1 : 2.
- x = (1×12 + 2×6) ÷ 3 = 8
- y = (1×2 + 2×5) ÷ 3 = 4
- Answer: (8, 4)
Common mistakes and misconceptions
- Swapping m and n in the section formula
- Forgetting the square root
Practice questions
- (Basic) Find the distance between A(5, 2) and B(11, 10).
- (Basic) Find the distance between A(-6, 4) and B(0, 12).
- (Standard) Find the distance between A(6, -6) and B(-2, 9).
- (Standard) Find the distance between A(6, 4) and B(1, 16).
- (Challenge) Find the point dividing A(2, -3) and B(6, -7) internally in the ratio 1 : 3.
- (Challenge) Find the point dividing A(2, -2) and B(5, -5) internally in the ratio 2 : 1.
Answer key with full working
- Q1: Δx = 6, Δy = 8 → AB = √(36 + 64) = √100 → AB = 10 units → Answer: 10 units
- Q2: Δx = 6, Δy = 8 → AB = √(36 + 64) = √100 → AB = 10 units → Answer: 10 units
- Q3: Δx = -8, Δy = 15 → AB = √(64 + 225) = √289 → AB = 17 units → Answer: 17 units
- Q4: Δx = -5, Δy = 12 → AB = √(25 + 144) = √169 → AB = 13 units → Answer: 13 units
- Q5: x = (1×6 + 3×2) ÷ 4 = 3 → y = (1×-7 + 3×-3) ÷ 4 = -4 → Answer: (3, -4)
- Q6: x = (2×5 + 1×2) ÷ 3 = 4 → y = (2×-5 + 1×-2) ÷ 3 = -4 → Answer: (4, -4)
Syllabus note
This skill is listed under "Coordinate Geometry" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is distance formula and section formula in?
"Coordinate Geometry", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.