Distance between two points

Distance Between Two Points

Introduction

  • The distance between two points in a coordinate system can be calculated using a mathematical formula derived from the Pythagorean theorem.
  • This concept is inherent to coordinate geometry, and understanding it can aid in grasping topics such as the equation of a line, the gradient of a line, and the properties of geometric shapes.

The Formula for the Distance Between Two Points

  • The formula for calculating the distance between two points, A(x1, y1) and B(x2, y2), on a coordinate system is defined as:

    D = √[(x2-x1)² + (y2-y1)²]

  • The formula essentially finds the length of the straight line (known as the line segment) connecting the two points A and B. The distance D is always a positive quantity or zero if the points are the same.

Process of Computing the Distance Between Two Points

  1. Identify the x and y coordinates for each point.
  2. Subtract the x-values (and then the y-values) of one point from the other and square each result.
  3. Add the two squared differences together.
  4. Take the square root of that sum to obtain the distance.

Examples

  • For two points A(2, 7) and B(5,3), the distance can be calculated as follows: D = √[(5-2)² + (3-7)²] = √[3² + (-4)²] = √[9+16] = √25 = 5
  • If calculating the distance between points A(-1, -2) and B(3, 2), the process would be: D = √[(3 - (-1))² + (2 - (-2))²] = √[(4)² + (4)²] = √ [16 + 16] = √32

Conclusion

  • Calculating the distance between two points is a fundamental skill in algebra and geometry. It provides the basis for understanding more complex problems involving distances and lines.
  • Regular practice with different coordinates can help you calculate these distances accurately and quickly, enhancing your problem-solving abilities within Mathematics.