Find the distance between two points on the coordinate plane using the Pythagorean theorem.
Formula for the Distance Between Two Points
Distance between A(x₁, y₁) and B(x₂, y₂):
AB = √{ (x₂-x₁)² + (y₂-y₁)² }
📘 Example ①
Find the distance between A(1, 2) and B(5, 5).
Answer: AB = √{ (5-1)² + (5-2)² } = √{ 16 + 9 } = √25 = 5
Find the distance between A(1, 2) and B(5, 5).
Answer: AB = √{ (5-1)² + (5-2)² } = √{ 16 + 9 } = √25 = 5
💡 Key Point
- Horizontal difference + vertical difference = hypotenuse (Pythagorean theorem)
- The order of subtraction can be reversed (because the differences are squared)
Practice Problems
- Find the distance between A(-1, 3) and B(3, 6).
- Find the distance between A(0, 0) and B(5, 12).
Answers and Explanations
- Answer: 5. (3-(-1))²+(6-3)²=16+9=25=5².
- Answer: 13. 5²+12²=25+144=169=13².