Find the distance between A\left(-1, -6\right)*A*(−1,−6)​ and B\left(7, -3\right)*B*(7,−3)​. Round your answer to two decimal places.

The distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in a 2D coordinate plane is given by the distance formula:

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

For points \( A(-1, -6) \) and \( B(7, -3) \):

\[
x_1 = -1, \quad y_1 = -6, \quad x_2 = 7, \quad y_2 = -3
\]

Substitute the values into the formula:

\[
d = \sqrt{(7 - (-1))^2 + (-3 - (-6))^2}
\]
\[
d = \sqrt{(7 + 1)^2 + (-3 + 6)^2}
\]
\[
d = \sqrt{8^2 + 3^2}
\]
\[
d = \sqrt{64 + 9}
\]
\[
d = \sqrt{73}
\]
\[
d \approx 8.54
\]

Thus, the distance between the points is approximately **8.54**.

Would you like more details or have any other questions?

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Here are 5 related questions for you:
1. How do you find the midpoint between two points?
2. Can you apply the distance formula in three dimensions?
3. What is the relationship between the distance formula and the Pythagorean theorem?
4. How does the slope between two points differ from the distance formula?
5. Can the distance formula be used for vectors?

**Tip:** Always double-check signs when plugging values into the distance formula to avoid common calculation errors.

Find the distance between A(-1, -6) and B(7, -3). Round your answer to two decimal places.

Find the distance between two points A(-1, -6) and B(7, -3) using the distance formula. This problem involves coordinate geometry and applying the Pythagorean Theorem. The solution is rounded to two decimal places, making it suitable for students in Grades 6-8.

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