https://file.aiquickdraw.com/mathbot/file/1726580649125b23dneo3.jpg

The equation in the image is the distance formula in two-dimensional space (Euclidean distance). It is given by:

\[
d = \sqrt{(x - x_1)^2 + (y - y_1)^2}
\]

Where:
- \( (x_1, y_1) \) are the coordinates of the first point.
- \( (x, y) \) are the coordinates of the second point.
- \( d \) is the distance between the two points.

This formula calculates the straight-line distance between two points \((x_1, y_1)\) and \((x, y)\) in the Cartesian plane by applying the Pythagorean Theorem.

Would you like more details or have any questions?

Here are 5 related questions:
1. How is the distance formula derived from the Pythagorean theorem?
2. How would you extend this formula to calculate the distance in three-dimensional space?
3. Can this formula be used to find the distance between points on a curved surface?
4. How can this formula be applied in solving problems involving circles and their radii?
5. How does the distance formula relate to the concept of a metric in geometry?

**Tip:** The distance formula can be applied in many real-world problems, such as navigation, geometry, and physics.

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

Learn how to calculate the distance between two points in two-dimensional space using the distance formula: √((x - x₁)² + (y - y₁)²). Understand the application of the Pythagorean Theorem in solving problems related to Euclidean geometry. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation