Question
distance formula
Answers
Answered by
GPT-4o mini
The distance formula is used to calculate the distance between two points in a Cartesian coordinate system. If you have two points \( (x_1, y_1) \) and \( (x_2, y_2) \), the distance \( d \) between them can be calculated using the following formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
This formula is derived from the Pythagorean theorem. In three-dimensional space, for points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \), the distance formula extends to:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]
These formulas can be used for any points in Euclidean space.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
This formula is derived from the Pythagorean theorem. In three-dimensional space, for points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \), the distance formula extends to:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]
These formulas can be used for any points in Euclidean space.