To find the distance \( AB \) between points \( A(3, 2) \) and \( B(2, -3) \), we can use the distance formula:

\[
AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

1. Substitute \( x_1 = 3 \), \( y_1 = 2 \), \( x_2 = 2 \), and \( y_2 = -3 \):

   \[
   AB = \sqrt{(2 - 3)^2 + (-3 - 2)^2}
   \]

2. Simplify inside the parentheses:

   \[
   AB = \sqrt{(-1)^2 + (-5)^2}
   \]

3. Calculate each square:

   \[
   AB = \sqrt{1 + 25}
   \]

4. Sum and take the square root:

   \[
   AB = \sqrt{26} \approx 5.1
   \]

So, the distance \( AB \) is approximately \( 5.1 \) units.

Would you like more details or have any questions?

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1. How do we derive the distance formula for points in a plane?
2. What are other ways to apply the distance formula in coordinate geometry?
3. How would the calculation change if one coordinate was 3D?
4. How is the midpoint of a line segment calculated?
5. How can we find the slope of the line joining two points?

**Tip:** Always square the differences first before adding in the distance formula.

Learn how to calculate the distance between two points A(3, 2) and B(2, -3) using the distance formula. This step-by-step solution explains the process, including substitution, simplification, and final calculation. Ideal for students in Grades 8-10 studying coordinate geometry.

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