# Applying the Distance Formula – Find the Distance Between the Points with Coordinates (-26, 0) and (95, 0).

## Find the Distance Between the Points with Coordinates (-26, 0) and (95, 0).

Applying the distance formula is a fundamental concept in mathematics that allows us to calculate the distance between two points on a coordinate plane. In this article, we will explore how to find the distance between two specific points with coordinates (-26, 0) and (95, 0).

To determine the distance between these two points, we can utilize the distance formula derived from the Pythagorean theorem. The formula states that the distance squared between two points (x1, y1) and (x2, y2) is equal to the square of the difference in their x-coordinates plus the square of the difference in their y-coordinates.

In our case, since both points lie on a horizontal line at y = 0, their y-coordinates are identical and therefore do not contribute to calculating the distance. Consequently, we only need to consider their x-coordinates. By plugging these values into our simplified formula and performing some calculations, we’ll be able to find out exactly how far apart these two points are.

Stay tuned as I walk you through step-by-step instructions on how to apply the distance formula and find the precise distance between (-26, 0) and (95, 0). So let’s get started!

## Calculating the Distance Between Two Points

One fundamental concept in mathematics is finding the distance between two points on a coordinate plane. In this section, we’ll explore how to apply the distance formula to determine the distance between two specific points: (-26, 0) and (95, 0).

To calculate the distance between these points, we can utilise the well-known distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 – x1)^2 + (y2 – y1)^2)

In our case, since both y-coordinates are 0, we only need to focus on the difference in x-coordinates. Plugging in these values into the formula gives us:

d = √((95 – (-26))^2 + (0 – 0)^2) = √(121^2 + 0) = √14641 ≈ 121

So, applying the distance formula reveals that the distance between (-26, 0) and (95, 0) is approximately 121 units.

Keep in mind that this approach can be applied to any pair of coordinates on a plane. By substituting different values into the formula based on your given coordinates, you can find distances accurately.

Understanding how to calculate distances between points using formulas like this one allows us to solve various real-world problems. For instance, it can be helpful for determining travel distances or measuring physical dimensions when dealing with coordinates.

By mastering these mathematical techniques and utilising them appropriately within practical scenarios, we enhance our problem-solving skills and expand our understanding of mathematical concepts.

Remember to always double-check your calculations and use caution when applying formulas. Accuracy is crucial when dealing with precise measurements or critical tasks that depend on correct calculations.

In conclusion, the process of calculating distances between two points on a coordinate plane involves applying the distance formula, which considers the differences in x and y coordinates. By substituting the given values into the formula, we can find accurate distances between points. This mathematical skill has practical applications in various fields and helps develop problem-solving abilities. So, don’t hesitate to apply the distance formula whenever you need to determine distances on a coordinate plane!

## Understanding the Distance Formula

When it comes to finding the distance between two points in a coordinate plane, the Distance Formula is an invaluable tool. In this section, we’ll dive into what exactly the Distance Formula is and how it can be applied to determine the distance between two given points.

The Distance Formula is derived from the Pythagorean Theorem and allows us to calculate the straight-line distance between any two points on a graph. It’s expressed as:

d = √((x2 – x1)² + (y2 – y1)²)

Let’s apply this formula to find the distance between two specific points: (-26, 0) and (95, 0). By substituting these values into our formula, we can determine their distance.

Using the coordinates (-26, 0) as (x1, y1), and (95, 0) as (x2, y2), we have:

d = √((95 – (-26))² + (0 – 0)²) = √(121² + 0) = √(14641) ≈ 121

Therefore, the distance between these two points is approximately 121 units.

The Distance Formula can be applied not only in Cartesian coordinates but also in three-dimensional space or even higher dimensions. It provides a straightforward method for determining distances regardless of whether they are positive or negative values.

By understanding and applying the Distance Formula correctly, you can easily find precise measurements between any given set of coordinates. Whether you’re working with simple geometry problems or complex real-life scenarios involving spatial relationships, this formula proves to be an essential tool in your mathematical arsenal.

Keep in mind that there are other alternative methods for calculating distances depending on specific situations. However, when dealing with pairs of points on a coordinate plane like we did here, using the Distance Formula remains one of the most efficient and accurate approaches.

So, armed with the knowledge of the Distance Formula, you’re now equipped to confidently find the distance between any two points in a coordinate system.