What is the length of AB
? Round your answer to the nearest hundredth.

A line segment graphed on a coordinate plane with endpoints at A negative 5 comma negative 4 and B negative 3 comma 3.

To find the length of the line segment \( AB \) with endpoints \( A(-5, -4) \) and \( B(-3, 3) \), we can use the **distance formula**:

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

Where:

- \( A(x_1, y_1) = (-5, -4) \)
- \( B(x_2, y_2) = (-3, 3) \)

Substituting the values:

\[
d = \sqrt{((-3) - (-5))^2 + (3 - (-4))^2}
\]

Simplify inside the parentheses:

\[
d = \sqrt{(2)^2 + (7)^2}
\]
\[
d = \sqrt{4 + 49}
\]
\[
d = \sqrt{53}
\]

Now, calculate the square root of 53:

\[
d \approx 7.28
\]

So, the length of \( AB \) is approximately **7.28** units.

Would you like more details on the process, or do you have any questions?

Here are 5 related questions for further exploration:
1. What is the midpoint of line segment \( AB \)?
2. How would the length of \( AB \) change if point \( A \) were moved?
3. What is the slope of the line passing through points \( A \) and \( B \)?
4. How can the Pythagorean theorem be used to verify the distance formula?
5. What are the coordinates of a point \( C \) such that \( ABC \) forms a right triangle?

**Tip:** When dealing with distances on a coordinate plane, remember to always check the units and use the distance formula for precise calculations.

What is the length of AB? Round your answer to the nearest hundredth. A line segment graphed on a coordinate plane with endpoints at A(-5, -4) and B(-3, 3).

Learn how to calculate the length of line segment AB with endpoints A(-5, -4) and B(-3, 3) using the distance formula. This solution includes step-by-step calculations and key geometric concepts, ideal for Grades 6-8 students.

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