The image asks for the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$.

The distance formula between these two points in a 2D plane is derived from the Pythagorean theorem and is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where:

• $d$ is the distance between the two points,
• $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would you apply the distance formula in three-dimensional space?
2. Can you explain how the distance formula relates to the Pythagorean theorem?
3. What is the midpoint formula between two points $(x_1, y_1)$ and $(x_2, y_2)$?
4. How can the distance formula be used to find if three points are collinear?
5. What happens to the distance formula if both points are the same?

Tip: Always square the differences between coordinates before summing them when using the distance formula to avoid errors with negative values.