Example 1 · level 1
Find the distance between the points (−2, 1) and (1, −3).
Show solution
- Δx = 1 − (−2) = 3, Δy = −3 − 1 = −4.
- d = √(9 + 16) = √25 = 5.
Answer: 5
CLASS 10 MATHS · COORDINATE GEOMETRY
Distance between two points
Distance between (x₁, y₁) and (x₂, y₂) = √[(x₂ − x₁)² + (y₂ − y₁)²].
Loading practice…
Worked examples
Example 2 · level 2
Find the distance between the points (6, −5) and (−6, 0).
Show solution
- Δx = −6 − 6 = −12, Δy = 0 − (−5) = 5.
- d = √(144 + 25) = √169 = 13.
Answer: 13
Example 3 · level 3
The distance between (3, −5) and (−1, k) is 5 units, and k < −5. Find k.
Show solution
- 16 + (k − (−5))² = 25
- (k − (−5))² = 9 → k − (−5) = −3
- k = −8.
Answer: -8