How to Calculate Distance Between Two Points Using a Formula

Calculating the distance between two points in a coordinate plane is a fundamental concept in mathematics that can be easily understood using the distance formula derived from the Pythagorean theorem. The distance formula is represented as:

$$d = √((x_2 - x_1)² + (y_2 - y_1)²)$$

Where (x1, y1) and (x2, y2) are the coordinates of the two points. Let's break this down step by step using the points (0, 5) and (-5, -6).

First, identify the coordinates:
- The first point is (0, 5), so we have:
- $x_1 = 0$
- $y_1 = 5$
- The second point is (-5, -6), so we have:
- $x_2 = -5$
- $y_2 = -6$

Next, we will calculate the differences in the x-coordinates and y-coordinates:
- Calculate $(x_2 - x_1)$:
- $(-5 - 0) = -5$
- Calculate $(y_2 - y_1)$:
- $(-6 - 5) = -11$

Now, we square these differences:
- $(x_2 - x_1)² = (-5)² = 25$
- $(y_2 - y_1)² = (-11)² = 121$

Now, plug these squared values back into the distance formula:

$$d = √(25 + 121)$$

This simplifies to:
$$d = √(146)$$

The final step is to calculate the square root of 146, which is approximately 12.083. Thus, the distance between the points (0, 5) and (-5, -6) is about 12.08 units.

Understanding how to calculate distances can be very useful in real-world applications, such as determining lengths on maps, navigation systems, or even in fields like engineering and physics. With practice, you will find that using the distance formula becomes quicker and more intuitive. If you have any questions or need more examples, feel free to ask!