To find the length of the line segment $AB$, we use the distance formula:

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

Given:

• $A(x_1, y_1) = (-4, 3)$
• $B(x_2, y_2) = (1, -3)$

Calculation:

$d = \sqrt{(1 - (-4))^2 + ((-3) - 3)^2}$ $d = \sqrt{(1 + 4)^2 + (-3 - 3)^2}$ $d = \sqrt{5^2 + (-6)^2}$ $d = \sqrt{25 + 36}$ $d = \sqrt{61}$

The approximate value of $\sqrt{61}$ is:

$\sqrt{61} \approx 7.81$

Final Answer:

The length of $AB$ is approximately 7.81 units.

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Would you like a detailed step-by-step breakdown of the calculation process or further clarification? 😊

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Here are 5 related questions for further practice:

1. How would you find the midpoint of segment $AB$?
2. If the slope of $AB$ is needed, how is it calculated?
3. Can you derive the equation of the line passing through points $A$ and $B$?
4. If point $C$ is the midpoint of $AB$, what are its coordinates?
5. How would you find the distance between a point and a line in the plane?

Tip: Always verify your calculations when working with square roots to avoid rounding errors!