# Distance Formula

#### Grade 8 Math Worksheets

**The distance formula is a mathematical expression used to calculate the distance between two points in a two- or three-dimensional space.**

Table of contents:

- Distance Formula
- Solved Examples
- FAQs

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## Distance Formula Worksheet PDF

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## Distance Formula

It is based on the Pythagorean theorem and is given by:

For two points (x1, y1) and (x2, y2) in a two-dimensional space:

Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2)

For two points (x1, y1, z1) and (x2, y2, z2) in a three-dimensional space:

Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

In both cases, the square root is taken to get the actual distance between the two points. The formula can be extended to higher dimensions as well.

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## Solved Examples

Example 1: Find the distance between the points (2, 4) and (6, 8) in a two-dimensional space.

Using the distance formula, we have:

Distance = sqrt((6 – 2)^2 + (8 – 4)^2)

Distance = sqrt(16 + 16)

Distance = sqrt(32)

Distance = 4sqrt(2)

Therefore, the distance between the points (2, 4) and (6, 8) is 4sqrt(2) units.

Example 2: Find the distance between the points (1, 2, 3) and (4, 5, 6) in a three-dimensional space.

Using the distance formula, we have:

Distance = sqrt((4 – 1)^2 + (5 – 2)^2 + (6 – 3)^2)

Distance = sqrt(9 + 9 + 9)

Distance = sqrt(27)

Distance = 3sqrt(3)

Therefore, the distance between the points (1, 2, 3) and (4, 5, 6) is 3sqrt(3) units.

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## Distance Formula FAQS

##### What is the distance formula used for?

The distance formula is used to calculate the distance between two points in a two- or three-dimensional space.

##### What is the formula for distance between two points in a two-dimensional space?

The formula for distance between two points (x1, y1) and (x2, y2) in a two-dimensional space is Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2).

##### What is the formula for distance between two points in a three-dimensional space?

The formula for distance between two points (x1, y1, z1) and (x2, y2, z2) in a three-dimensional space is Distance = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2).

##### What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

##### How do you calculate the distance between two points on a coordinate plane?

To calculate the distance between two points on a coordinate plane, you can use the distance formula. First, you identify the coordinates of the two points, and then you substitute them into the formula to get the distance between them.

##### Can the distance formula be used for higher dimensions?

Yes, the distance formula can be extended to higher dimensions beyond three dimensions. However, the formula becomes more complex as the number of dimensions increases.

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