## Introduction of Distance Formula Calculator

Distance formula calculator calculates the distance between two given points. It may be the distance between the two cities or maybe from your location to any other place. Actually the 1 D space between two points is called distance. Even the meaning of distance is a little longer than it. Its concept is not limited but extends beyond the length that is an innovation behind Einstein’s theory of relativity.

## Distance between two points

In a Cartesian grid to measure a line segment that is either vertical or horizontal simple enough. You can count the distance either up and down the y-axis or across the x-axis but what about diagonal lines. You can use the distance formula calculator to calculate any line segment. If you know the coordinates of the two endpoints, you will be mentally constructing a right triangle, using the diagonal as it were a hypotenuse.

## How does a distance calculator work?

In distance calculator, you just take two x coordinates and two y coordinates at given space in a calculator. It will automatically calculate the distance between those two coordinates (points) and show you result stepwise. So we can say it to measure the distance between two points calculator.

To make the calculation of distance, you just need those two points. These two points are described by their coordinates. In 2D space for each point, we require two unique coordinates. If you want to calculate the distance between those two points in 1 D space, yeah you can find the result by using distance formula calculator with miner setting one of the coordinates for both points.

At the next step, for mathematical accuracy and preciseness, you must define the type of space in which you are doing work. It will not take much time as well as easier than your thinking. If you don’t know about space in which you are working then it will be default settled Euclidean space.

## Distance Formula

There are many different ways to determine the distance between two objects. In addition, there are just as many tools that you can use. Mathematically, if you want to determine the distance between two points on a coordinate plane, you use the distance formula.

$$D = ?(x2 – x1)^2 + (y2 – y1)^2$$.

$$d= \sqrt{(x^2-x^1)^2+(y^2-y^1)^2}$$

### Example 1:

When you know the coordinates of the two points that you are trying to find the distance between, just substitute into the equation.

If doesn’t really matter which point is **(x1, y1)** or which one is **(x2, y2)**, just so long as you keep them together. Which set you use for 1, use it for both **x1 **and **y1**, and whichever set you use as 2, use both **x2** and **y2** from that set.

**Step 1:**Find the distance between the given points on the above given graph. The coordinates of the two points are:

$$(x1 , y1) = (2, 5)$$

$$(x2, y2 ) = (9, 8)$$

**Step 2:** To solve this equation you just need to substitute the numbers into the distance formula.

$$d= \sqrt{(x^2-x^1)^2+(y^2-y^1)^2}$$

$$d= \sqrt{(9-2)^2+(8-5)^2}$$

$$d= \sqrt{(7)^2+(3)^2}$$

$$d= \sqrt(58)$$

$$d= 7.6$$

## Example 2:

Find the distance from one point to another on the given graph.

In this example, the points are **(-1,2)** and **(2,1)**.

$$(x1 , y1) = (-1, 2)$$

$$(x2 , y2) = (2 , 1)$$

By using the formula

$$d= \sqrt{(x^2-x^1)^2+(y^2-y^1)^2}$$

Let’s plugin values to the formula and then simplify it just like example 1.

$$d= \sqrt{(2-(-1))^2+(1-2)^2}$$

$$d= \sqrt{(2+1)^2+(-1)^2}$$

$$d= \sqrt{(3)^2+(1)}$$

$$d= \sqrt{9+1}$$

$$d= \sqrt{10}$$

$$d= 3.1$$

When using the distance formula for negative numbers, it’s very important to work carefully. So you don’t lose the negative along the way.

## Terminologies

As math is an abstract and challenging subject, there are most of terms which we can’t understand. So, I consider necessary to make clear these terms, in which sense these have been played role in distance calculation formula. First of all, if we talk about** Pythagorean Theorem**, the distance formula actually is a presentation of the Pythagorean Theorem. As;

$$\text{Pythagorean Theorem} = a^2+b^2 = c^2$$

$$d^2 = (x^2 – x^1)^2+(y^2 – y^1)^2$$

$$\text{Distance of two points} = d =\sqrt{ (x^2 – x^1)^2+(y^2 – y^1)^2}$$

Next, we discuss about the word **Hypotenuse**, is actually a geometrical term which mean the longest side of a right- angled triangle. E.g.

$$\text{Pythagorean Theorem} = a^2+b^2 = c^2$$

**a = side**

**b = side**

**c = hypotenuse**

Now, we move toward next term, Cartesian coordinate system, specifies each point distinctively in a plane by a set of numerical coordinates. These are the signed distances from two fixed perpendicular oriented lines, which will be measured in the same unit of length.

In this article, we have learned about the distance formula to find the distance from a known point to another known point. After working your way through this article, you would be able to understand the working of distance formula calculator. Hopefully this tool will provide you the better assistance to apply the distance formula to calculate the distance between two given points.

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