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The image you uploaded shows the equation for calculating the distance between two points on a Cartesian plane. Specifically, it is using the distance formula: \( r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

In your equation:
- \( x_1 = -3.5 \)
- \( y_1 = 0 \) (since there is no y-value with -3.5, it is assumed to be on the x-axis)
- \( x_2 = 0 \) (since there is no x-value with 2.5, it is assumed to be on the y-axis)
- \( y_2 = 2.5 \)

The formula provided calculates the distance as follows:
\[ r = \sqrt{(-3.5 - 0)^2 + (0 - 2.5)^2} \]
\[ r = \sqrt{(-3.5)^2 + (-2.5)^2} \]
\[ r = \sqrt{12.25 + 6.25} \]
\[ r = \sqrt{18.5} \]

Thus, the distance \( r \) is \( \sqrt{18.5} \).

Do you need the numerical value of this square root, or is there anything else you'd like to know? Here are some further questions you might consider:

1. What are the coordinates of the midpoint between these two points?
2. How does the distance change if one of the points moves?
3. What if this calculation were in three dimensions?
4. Would you like to calculate the distance using a different pair of points?
5. How can this concept be applied to real-life scenarios?

Tip: When using the distance formula, always check the signs (+ or -) of your coordinates carefully to avoid errors in your final calculation.

Calculate the distance between two points on a Cartesian plane using the given values.

Learn how to calculate the distance between two points using the distance formula, derived from the Pythagorean theorem, in a Cartesian coordinate system. This guide provides a step-by-step solution to understanding and applying the distance formula effectively.

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