Table of Contents: -

• 1. Introduction to the distance between two points
• 2. What is the Formulae used ?
• 3. How do I calculate the distance between two points ?
• 4. Why choose our Distance between two points in 2-D & 3-D Calculator?
• 5. A Video for explaining this concept
• 6. How to use this calculator ?
• 7. Solved Examples
• 8. Frequently Asked Questions (FAQs)
• 9. What are the real-life applications?
• 10. Conclusion

1. Introduction to the distance between two points: -

• Understanding the concept of distance is essential in various fields such as mathematics, physics, engineering, and computer science. In both two-dimensional (2D) and three-dimensional (3D) spaces, the distance between two points plays a crucial role in determining relationships, measurements, and calculations.

• Definition: -

  The distance between two points in 2D or 3D is a numerical value representing the length of the straight line segment that connects those points. It measures the spatial separation between the points and provides a fundamental metric for analyzing geometric relationships.

2. What is the Formulae used?

• To calculate the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in 2D space, we can utilize the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two other sides.
• The distance formula for the $\bold{distance \space in \space 2D}$ is given as:
• d = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
• Similarly, $\bold{distance \space in \space 3D}$ space, the distance formula to calculate the distance between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ can be derived using the same principle:
• d = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

Click this to access distance between two points calculator

3. How do I calculate the distance between two points?

• Identify the given cartesian coordinates $(x_1, y_1)$ & $(x_2, y_2)$ of the given points.
• use the distance formula to calculate the distance between both points.

4. Why choose our Distance between two points in 2-D & 3-D Calculator?

• Ease to Use: -

  Our calculator provides a user-friendly interface that makes it accessible to both students and professionals. You can quickly input your square matrix and obtain the matrix of minors within a fraction of a second.

• Time-Saving By automating the calculation process: -

  Our calculator saves you valuable time and effort. You no longer need to manually calculate each cofactor, making complex matrix operations more efficient.

• Accuracy and Precision: -

  Our calculator ensures accurate results by performing calculations based on established mathematical formulas and algorithms. It eliminates the possibility of human error associated with manual calculations.

• Versatility: -

  Our calculator can handle all types of input values like integers, fractions, or any real number.

• Complementary Resources: -

  Alongside this calculator, our website offers additional calculators related to coordinate geometry and algebric operations. These calculators can further enhance your understanding and proficiency.

5. A video based on the concept of how to find the distance between two points using the distance formula.

6. How to use this calculator

• This calculator will help you to find the distance between two points in 2-D & 3-D.
• In the given input boxes you have to put the coordinates value for x, y and z for both points.
• After clicking on the Calculate button, a step-by-step solution will be displayed on the screen. You can access, download, and share the solution.

7. Solved Examples

Question: - 1

• Using the distance formula, calculate the distance between two points A (2, 3) and B (5, 7).

Solution: -

• By using distance formula, d = $\sqrt{(5 - 2)^2 + (7 - 3)^2}$ = $\sqrt{25}$ = 5

Question: - 2

• Using the distance formula, calculate the distance between two points A (1, 2, 3) and B (4, 5, 7).

Solution: -

• By using distance formula d = $\sqrt{(4 - 1)^2 + (5 - 2)^2 + (7 - 3)^2}$ = $\sqrt{34}$.

8. Frequently Asked Questions (FAQs):-

$\bullet$ What is the significance of calculating distances in 2D and 3D spaces?

• Calculating distances helps measure spatial separation, determine lengths, define relationships, and solve geometric problems in various fields.

$\bullet$ Can the distance between two points ever be negative?

• No, the distance between two points is always a positive value or zero. It represents the magnitude of separation, which cannot be negative.

$\bullet$ Is there any alternative formula to calculate the distance between two points?

• The distance formula derived from the Pythagorean theorem is the most commonly used method to calculate distances between points in 2D and 3D spaces.

$\bullet$ What are the Coordinates of a point?

• In Euclidean geometry, we came across the points that were positioned in the plane. Their coordinates along the x-axis and y-axis define these points. Therefore, the coordinates of a point are a pair of values that exactly define the location of that point in the Argand plane.

$\bullet$ What is the shortest distance between two points?

• The shortest distance between two points is a straight line connecting them. But this definition only applies to flat surfaces or spaces. In a sphere, for example, the shortest distance between two points is an arc called distance along the circular arc.

9. What are the real-life applications?

$\space \space$ 2D Applications:

• Navigation and GPS
• Surveying
• Computer Graphics
• Physics
• Geometry

$\space \space$ 3D Applications

• Computer Graphics and 3D Modeling
• Astronomy
• Engineering and Architecture
• Robotics
• Medical Imaging
• Geographic Information Systems (GIS)
• Physics and Engineering Mechanics

10. Conclusion

• Understanding the concept of distance between two points in 2D and 3D spaces is vital for numerous applications. By applying the distance formula derived from the Pythagorean theorem, we can calculate the length of the straight line segment connecting two points accurately. This knowledge has practical implications in mathematics, physics, engineering, computer science, and many other fields. By mastering the concept of distance, we can explore and analyze the geometric relationships that exist in our world, enabling us to solve a wide range of problems effectively.

This blog is Written by: - $\fcolorbox{red}{lightyellow}{\color{red}{Neetesh Kumar}}$

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