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Introduction

In this tutorial, we will learn how to calculate the distance between two points in a coordinate system, a fundamental concept in mathematics, particularly useful in geometry. This guide is based on the insights provided by Kak Dhanar, a Master Teacher in Mathematics from Ruangguru. Understanding this concept is essential for solving various mathematical problems and real-world applications.

Step 1: Understanding the Coordinate System

• Familiarize yourself with the Cartesian coordinate system, which consists of:
  • X-axis (horizontal)
  • Y-axis (vertical)
• Each point on this plane is represented by coordinates in the form (x, y).

Step 2: Formula for Distance Between Two Points

• The distance (d) between two points (A(x_1, y_1)) and (B(x_2, y_2)) is calculated using the distance formula:

  [ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

• Here’s how to use the formula:

  • Subtract the x-coordinates: (x_2 - x_1)
  • Subtract the y-coordinates: (y_2 - y_1)
  • Square both results.
  • Add the squared results together.
  • Take the square root of the sum.

Step 3: Example Calculation

• Let’s calculate the distance between points (A(3, 4)) and (B(7, 1)):
  • Calculate (x_2 - x_1 = 7 - 3 = 4)
  • Calculate (y_2 - y_1 = 1 - 4 = -3)
  • Square the differences: (4^2 = 16) and ((-3)^2 = 9)
  • Add the squared values: (16 + 9 = 25)
  • Take the square root: (d = \sqrt{25} = 5)
• Therefore, the distance between points A and B is 5 units.

Step 4: Practical Applications

• Use this distance calculation in various scenarios:
  • Geometry: Determine the length of line segments.
  • Physics: Calculate the displacement between two locations.
  • Computer Graphics: Measure distances between objects on a screen.

Conclusion

Calculating the distance between two points is a straightforward yet powerful tool in mathematics. By understanding the coordinate system and applying the distance formula, you can solve numerous problems across different fields. To further enhance your skills, practice with different points and explore related concepts such as the midpoint and slope of a line. For more resources, consider downloading the Ruangguru app for additional tutorials and support.