How To Find The Distance Between 2 Points In 3D Space

TL;DR

Learn how to calculate the distance between two points in 3D space using the distance formula, which involves finding the square root of the sum of the squares of the differences of the x, y, and z values.

Transcript

in this video we're going to talk about how to find the distance between two points and also how to understand how the formula works so let's begin so let's say if we want to find the distance between the point one comma two comma negative five and the second point which is four comma six comma seven so what's a simple way to find the distance betw... Read More

Key Insights

• 🟨 The distance formula for finding the distance between two points in 3D space involves taking the square root of the sum of the squares of the differences in the x, y, and z values.
• 😥 Graphically representing the points on a 3D coordinate system allows for a visual understanding of how the distances are calculated using the differences in coordinates.
• 🗯️ The distance formula can be derived from the Pythagorean theorem for right triangles.

Questions & Answers

Q: What is the distance formula used to calculate the distance between two points in 3D space?

The distance formula involves finding the square root of the sum of the squares of the differences between the x, y, and z values of the two points. It is derived from the Pythagorean theorem for right triangles.

Q: How can the distance between two points be visually represented on a 3D coordinate system?

On a 3D coordinate system, the distance between two points can be represented by drawing lines parallel to the x, y, and z axes. The length of these lines represents the differences in x, y, and z values, which can be used to calculate the distance using the distance formula.

Q: Can the distance formula be used for points in any number of dimensions?

Yes, the distance formula can be used to find the distance between points in any number of dimensions. The formula remains the same: taking the square root of the sum of the squares of the differences of the coordinates.

Q: What is the significance of the square root in the distance formula?

The square root is applied to the sum of the squares in the distance formula to ensure that the result represents the actual distance between the two points. Without the square root, the distance would be the sum of the squares, which does not give a meaningful distance measurement.

Summary & Key Takeaways

• The video discusses how to find the distance between two points in 3D space by using the distance formula.

• The formula involves taking the square root of the sum of the squares of the differences between the x, y, and z values of the two points.

• The video also visually explains how to plot the points on a 3D coordinate system and calculate the distances between them.