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.