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.