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Calculate the Distance Between Two Points Online

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How to Find Distance Between Two Points With Formula and Steps

Distance Between Two Points Calculator

Point 1 (x₁, y₁):

Point 2 (x₂, y₂):

Include z-coordinates (3D)

Example: (0,0) & (3,4) | (2,-1) & (7,3) | 3D: (1,5,2) & (8,9,6)

What is Distance Between Two Points Calculator?

This Distance Between Two Points Calculator helps you instantly find the straight-line distance between any two points on a coordinate plane or in 3D space. Simply enter the coordinates, and the tool delivers the exact result with a clear breakdown.

Whether you're working through maths homework or tackling geometry in real life, this calculator simplifies calculations that would otherwise take valuable time. Its step-by-step method and visual output ensure that you learn and verify the solution process easily.

Formula Behind Distance Between Two Points Calculator

For two points on a 2D plane, the distance is calculated with the formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²], derived from the Pythagoras’ theorem. In 3D space, the formula extends to: d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²], accounting for all three coordinate differences.

Distance Between Two Points Conversion Table

Points	Calculated Distance
(0, 0), (3, 4)	5
(2, -1), (7, 3)	6.4031
(1, 5, 2), (8, 9, 6)	8.9443
(-2, 7), (4, -5)	13.416
(-3, -2, 0), (0, 2, 6)	7.8102

Steps to Use Distance Between Two Points Calculator

Enter the coordinates for each point. For 3D calculations, include z-values.
Click "Calculate" to process your values.
Instantly view the distance, stepwise solution, and 2D visualisation.

Why Use Vedantu’s Distance Between Two Points Calculator?

Vedantu’s calculator delivers instant, accurate results—saving you time and reducing calculation errors. The tool adapts for 2D and 3D geometry, so it's suitable for everything from school basics to advanced applications.

You get step-by-step workings and a visual graph, aiding understanding and confidence. Plus, clickable examples and touch-friendly design ensure a seamless experience on any device.

Applications of Distance Between Two Points Calculator

Calculating the distance between two points is essential in coordinate geometry, construction, engineering drawings, physics problems, and navigation. It is frequently used to determine direct routes and object separations.

In mapping technology, surveying, and even in digital design, this formula finds distances in various contexts. If you’re working on topics like the Pythagorean theorem or coordinate geometry, this tool is invaluable.

For further support, check our Class 8 maths formulas and advanced concepts like equation of a line and 3D geometry on Vedantu.

FAQs on Calculate the Distance Between Two Points Online

1. How do you calculate the distance between two points?

The distance between two points is calculated using the distance formula, derived from the Pythagorean theorem. For two points (x₁, y₁) and (x₂, y₂) in a 2D plane, the distance is √((x₂ - x₁)² + (y₂ - y₁)²) . For 3D points (x₁, y₁, z₁) and (x₂, y₂, z₂), it's √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) . This formula gives the straight-line distance between the points.

2. What is the distance formula in geometry?

The distance formula is a mathematical equation used to determine the distance between two points in a coordinate system. In a 2D plane, the formula is: Distance = √((x₂ - x₁)² + (y₂ - y₁)²) where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points. For 3D space, a z-coordinate is added: Distance = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) .

3. How to find the distance between two points step by step?

1. **Identify the coordinates:** Write down the x and y (and z for 3D) coordinates of each point. 2. **Apply the formula:** Substitute the coordinates into the appropriate distance formula (2D or 3D). 3. **Calculate the differences:** Subtract the x-coordinates, y-coordinates, and z-coordinates (if applicable). 4. **Square the differences:** Square each difference obtained in step 3. 5. **Sum the squares:** Add the squared differences together. 6. **Take the square root:** Find the square root of the sum from step 5 to get the final distance.

4. What is the formula for the distance between two points in 3D space?

The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in 3D space is given by the formula: Distance = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²) This extends the 2D distance formula to include the z-coordinate.

5. How to use the distance formula for coordinates?

Simply substitute the x and y coordinates of your two points into the distance formula: √((x₂ - x₁)² + (y₂ - y₁)²) . For example, if point 1 is (1, 2) and point 2 is (4, 6), the distance would be √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.

6. What are some real-life applications of the distance formula?

The distance formula has many real-world applications, including: • **GPS Navigation:** Calculating distances between locations. • **Mapping and Surveying:** Determining distances between points on maps or land. • **Construction and Engineering:** Measuring distances for building projects and infrastructure. • **Physics:** Calculating distances in various physical phenomena. • **Computer Graphics:** Determining distances between points in 3D models and games.

7. How is the distance formula related to the Pythagorean theorem?

The distance formula is a direct application of the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. The distance between two points represents the hypotenuse of a right-angled triangle formed by the difference in x-coordinates and y-coordinates.

8. What is the distance between (2, 3) and (7, 8)?

Using the distance formula: √((7 - 2)² + (8 - 3)²) = √(25 + 25) = √50 ≈ 7.07 units. The distance between the points (2,3) and (7,8) is approximately 7.07 units.

9. Can I use this calculator for 3D points?

Yes, many distance calculators support both 2D and 3D coordinates. You'll need to input the x, y, and z coordinates for each point. The calculator will then use the 3D distance formula to compute the distance.

10. What if I have points on a number line?

The distance between two points on a number line is simply the absolute difference between their coordinates. For example, the distance between 2 and 7 is |7 - 2| = 5. This is a simplified version of the distance formula.

11. Explain the concept of Euclidean distance.

Euclidean distance is the straight-line distance between two points in Euclidean space. The distance formula we use to calculate the distance between points is a direct calculation of this Euclidean distance. It's the most common way to measure distance in geometry and many applications.