Calculating the Distance Between Two Points: A Step-by-Step Guide

Coordinate geometry is a fundamental concept in mathematics, and understanding how to calculate the distance between two points is a crucial skill. In this article, you will learn how to use the distance formula to find the distance between two given points on a coordinate plane.

Understanding the Distance Formula

The distance formula is derived from the Pythagorean theorem and is given by:

d √((x2 - x1)2 (y2 - y1)2)

where d represents the distance between the two points, (x1, y1) and (x2, y2), in a two-dimensional coordinate plane.

Application of the Distance Formula

Let's use the points A(4, 3) and B(1, -1) as an example to understand how to apply the distance formula step by step.

Step 1: Identify the Coordinates

The coordinates of point A are (4, 3)

The coordinates of point B are (1, -1)

Step 2: Plug the Coordinates into the Formula

Let's substitute the coordinates into the distance formula.

d √((1 - 4)2 (-1 - 3)2)

Step 3: Simplify the Expression

Now, we simplify the expression inside the square root:

d √((-3)2 (-4)2)

d √(9 16)

d √25

d 5

This calculation shows that the distance between points A and B is 5 units.

Conclusion

Understanding and applying the distance formula is essential in coordinate geometry. It is widely used in various fields, including physics, engineering, and computer science. Mastery of this concept can help you solve complex problems and enhance your analytical skills.

Additional Resources

For more information on coordinate geometry and the distance formula, explore the following resources:

Math is Fun: Distance Between Two Points Khan Academy: Distance Between Two Points Math Warehouse: Distance Formula Notes