Find the length of AB¯¯¯¯¯¯¯¯
 to the nearest hundredth. point a is (-5,-4) Point b is (-3,3)

To find the length of line segment \( AB \), we use the distance formula:

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

Where:
- \( (x_1, y_1) \) is point \( A (-5, -4) \)
- \( (x_2, y_2) \) is point \( B (-3, 3) \)

Substitute the coordinates into the formula:

\[
d = \sqrt{(-3 - (-5))^2 + (3 - (-4))^2}
\]
\[
d = \sqrt{(-3 + 5)^2 + (3 + 4)^2}
\]
\[
d = \sqrt{(2)^2 + (7)^2}
\]
\[
d = \sqrt{4 + 49} = \sqrt{53}
\]
\[
d \approx 7.28
\]

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

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we find the midpoint of \( AB \)?
2. How would the distance change if the coordinates of \( A \) and \( B \) were swapped?
3. What is the equation of the line passing through \( A \) and \( B \)?
4. How do we compute the slope of the line segment \( AB \)?
5. Can we calculate the distance between any two points in 3D space using a similar method?

**Tip:** The distance formula is derived from the Pythagorean Theorem. You are essentially calculating the hypotenuse of a right triangle formed by the horizontal and vertical distances between two points.

Find the length of AB¯¯¯¯¯¯¯¯ to the nearest hundredth. Point A is (-5, -4) and Point B is (-3, 3).

Learn how to calculate the distance between two points A(-5, -4) and B(-3, 3) using the distance formula. This step-by-step guide applies key geometric concepts and the Pythagorean Theorem. Ideal for students in Grades 7-10.

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