Hey Mate Welcome to Math Formula Calculators! On this website you will get each and every Basic and advanced formula of Mathematics. The Distance Formula Calculator, Midpoint formula calculator, Trig Identities and many others. The applications of the Math in our daily life are beyond the scope. That’s why we decided to create a roof by the Name of Math Formula Calculators where you can easily find basic & advanced Math Formula Calculators.
Distance Formula Calculator
In Math Distance Formula is one of the effects and most useful tool in order to find out the distance between two different points. You will be amazed to know that the distance formula is actually derived from the Pythagorean Theorem which is
a^2 + b^2 = c^2 or a2 +b2 = c2
in which the c is the longest side of the right-angled triangle which is also called the hypotenuse and a & b are the base and altitude respectively. The c is also known as the straight-line distance between a & b. That’s why most of the mathematician claims that this is a simple Pythagorean Theorem. If you really want to know how the Distance Formula is derived from the Pythagorean Theorem then we must recommend you to follow up the link of How to Derive Distance Formula by using Pythagorean Theorem.
The Distance Formula
Here comes the legendary Distance Formula Calculator. It is highly recommended to go through the whole guide in order to explore more & more about distance formula calculator.
If you want to learn how to Drive Distance Formula based on the Pythagorean Theorem where the d of distance is the d of the hypotenuse of Right-Angled Triangle.
The above expression (x_2 – x_1) x2-x1 can also be read as “change in xX”
The second expression (y_2 – y_1) y2-y1 can also be read as the “change in yY”
Daily Life Examples of Distance Formula
Example # 1: Find out the distance between the following two points.
P1 = (-3, 2)
P2 = (3, 5).
First of all, you need to label all the coordinates of each point accurately & then you have to substitute the values properly in the distance Formula which is mentioned above.
According to the Cartesian Coordinate System the first point is lying in the 2nd Quadrant because X is negative and Y is positive. Similarly, the second point is (3,5) lies in the 1st quadrant because both are positive. Now we have to find the distance between these 2 points.
Here comes the Step by Step Calculation of Distance Formula Between 2 points.
Now we can say that the distance between the P1 (-3, 2) and P2 (3, 5) is 3 Sqrt 5. Here comes the graphical representation of the Points and distance between them.
Example # 2 – Find out the distance between the following points.
P1 = (-1, -1)
P2 = (4, -5)
If we look at the point 1 then we can easily say that the P1 lies in the 3rd cartesian quadrant where both x & y are negatives, while on the other hand the point 2 lies in the 4th Cartesian Quadrant where x is positive & y is negative.
All you need is to substitute the values of x1, y1, x2, and y2 in the formula.
Now we can say that the distance between the P1 (-1, -1) and P2 (4, -5) is Sqrt 41. Here comes the graphical representation of the Points and distance between them.
Example # 3 – Find the distance between the following
P1 = (-4, -3)
P2 = (4, 3)
Let me put a question what happens if we switch the points which calculating the distance. Will it affect the final outcome or results or not? Post your answer in comments.
Well let us explain a bit to you. The Distance Formula is squaring the difference of respective x1, x2, and y1, y2 values which means that’s there will be no difference if you change the xx which is also called the delta xx or the change in yy which is also called delta yy will be negative. It is because of when we eventually square the value it results always comes out a positive value.
Still if you are not clear with the things lets prove it with the help of answer by solving the problem in 2 possible ways.
The very 1st solution depicts clearly the common way because in this solution we defined which point is the first & which is the second and its totally based on the order in which it appears in the problem. Whereas in the 2nd solution, we basically switch the points, P2 becomes the P1, and P1 becomes the P2 respectively.
- Solution 2:
Here comes the 2nd solution in which we have switched the points.
It is very clear from the above solutions that both of the calculations arrived at the same results or outcome which the the 10, d=10. Here comes the graphical representation of the example solved above.
Example # 4: Find out the radius of the circle with the help of diameter whose endpoints are following.
P1 = (-7, 1)
P2 = (1, 3)
Note – You may know that the diameter of a circle is twice in length as compared to its radius. So, we can also write the radius is the half of the length of diameter.
Here comes the detail of the plan! We are provided with the 2 endpoints which are the endpoints of the diameter. We can easily use the distance formula it orders to find the length of the diameter. Then we have to divide the resultant value by 2 in order to get the radius of the circle.
The given points are P1 = (-7,1) which belongs to the second quadrant and the second point P2 = (1, 3) which belongs to the 1st quadrant. By putting the values in the distance formula.
Now we have to solve it in order to get the value of the radius. To do so, divide the result with 2 or multiple it with ½.
In the graphical representation of the given data the blue dots clearly representing the endpoints of the diameter and the green dot is the center of the circle or the midpoint of the diameter. The distance from the green dot to either side left or right till blue dot is the radius of the circle.