Quick answer: The distance between (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²]. It comes from Pythagoras applied to horizontal and vertical differences.
Worked example
Find the distance from A(−2, 3) to B(4, −5).
- Horizontal difference is 4 − (−2) = 6.
- Vertical difference is −5 − 3 = −8.
- Distance = √(6² + (−8)²) = √100 = 10 units.
Check the result
Reversing the points gives differences −6 and 8, whose squares give the same result.
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Common mistake to avoid
Square each difference before adding. √(a² + b²) is not generally a + b.
Try it yourself
1. Find the distance from (0, 0) to (3, 4). 2. Find the distance from (1, 2) to (4, 6).
Answers and reasoning
1. √(9 + 16) = 5. 2. The differences are 3 and 4, so the distance is also 5 units.
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