Distance Formula

beginneralgebracoordinate geometry

Calculates the distance between two points in a coordinate plane

The Formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Variables & Symbols

d

Distance between points

Unit: units

(x₁, y₁)

Coordinates of first point

(x₂, y₂)

Coordinates of second point

When to Use This Formula

  • Finding distance between two points on a graph
  • Calculating length of line segments
  • In geometry problems involving circles
  • Navigation and mapping applications

Worked Examples

Example 1

Problem:

Find distance between (2, 3) and (5, 7)

Solution: d = 5 units

Step-by-Step:

1

Identify: (x₁,y₁) = (2,3), (x₂,y₂) = (5,7)

2

d = √[(5-2)² + (7-3)²]

3

d = √[3² + 4²] = √[9 + 16]

4

d = √25 = 5 units

Common Mistakes to Avoid

  • Forgetting to square the differences
  • Not taking the square root at the end
  • Mixing up x and y coordinates

Real-World Applications

1

GPS navigation and route planning

2

Computer graphics and game development

3

Astronomy - calculating distances between celestial objects

4

Architecture and surveying

Practice Problems

Problem 1: Distance between (0,0) and (3,4)

Show Answer

Answer: 5 units

Problem 2: Distance between (-1,2) and (2,6)

Show Answer

Answer: 5 units

Related Formulas

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Tags:

algebracoordinate geometrydistancepoints

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