The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is applicable in two or three-dimensional space. The formula is as follows:
For two points (x₁, y₁) and (x₂, y₂) in a two-dimensional plane:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's break down the formula step by step:
1. Subtract the x-coordinates: (x₂ - x₁)
This step calculates the difference between the x-coordinates of the two points.
2. Square the result of step 1: (x₂ - x₁)²
We square the result obtained in step 1 to eliminate negative values and ensure the distance is always positive.
3. Subtract the y-coordinates: (y₂ - y₁)
Similar to step 1, this step calculates the difference between the y-coordinates of the two points.
4. Square the result of step 3: (y₂ - y₁)²
We square the result obtained in step 3 to eliminate negative values and ensure the distance is always positive.
In this case, the formula follows the same principles as the two-dimensional formula but includes an additional term to account for the difference in z-coordinates.
By using the distance formula, we can determine the precise distance between any two points in space, whether it's on a flat plane or in three-dimensional space.
Answers & Comments
Answer:
The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is applicable in two or three-dimensional space. The formula is as follows:
For two points (x₁, y₁) and (x₂, y₂) in a two-dimensional plane:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's break down the formula step by step:
1. Subtract the x-coordinates: (x₂ - x₁)
This step calculates the difference between the x-coordinates of the two points.
2. Square the result of step 1: (x₂ - x₁)²
We square the result obtained in step 1 to eliminate negative values and ensure the distance is always positive.
3. Subtract the y-coordinates: (y₂ - y₁)
Similar to step 1, this step calculates the difference between the y-coordinates of the two points.
4. Square the result of step 3: (y₂ - y₁)²
We square the result obtained in step 3 to eliminate negative values and ensure the distance is always positive.
5. Add the squared differences: (x₂ - x₁)² + (y₂ - y₁)²
This step adds the squared differences of the x and y coordinates.
6. Take the square root: √((x₂ - x₁)² + (y₂ - y₁)²)
Finally, we take the square root of the sum of squared differences to obtain the actual distance between the two points.
The distance formula can also be extended to three-dimensional space by adding the difference in z-coordinates squared:
For two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional space:
Distance = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
In this case, the formula follows the same principles as the two-dimensional formula but includes an additional term to account for the difference in z-coordinates.
By using the distance formula, we can determine the precise distance between any two points in space, whether it's on a flat plane or in three-dimensional space.
Verified answer
hopefully the attachment will help you