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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.

Write the distance formula between points (x₁, y₁) and (x₂, y₂).

Learn how to calculate the distance between two points (x₁, y₁) and (x₂, y₂) using the distance formula derived from the Pythagorean theorem. This concept is essential in coordinate geometry and is suitable for students in Grades 9-12.

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