To find the distance between the two points on the coordinate plane, we use the distance formula:

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

From the image, we can identify the coordinates of the two points:

• The upper point is at $(-6, 4)$
• The lower point is at $(-3, -4)$

Now, applying the distance formula:

$d = \sqrt{((-3) - (-6))^2 + ((-4) - 4)^2}$

Simplifying the expression:

$d = \sqrt{(3)^2 + (-8)^2} = \sqrt{9 + 64} = \sqrt{73}$

None of the provided options include $\sqrt{73}$, but the closest approximation is around 8.54, which makes 7 or 9 possible answers, with 9 being closer.

Thus, the correct answer is likely B: 9.

Would you like further details on any step, or have any other questions?

Here are some related questions to expand understanding:

1. How do we simplify square roots when they are not perfect squares?
2. What is the difference between Euclidean distance and other distance metrics?
3. Can the distance between points ever be negative?
4. How do you plot points with negative coordinates on a graph?
5. What is the meaning of each part of the distance formula?

Tip: Always check your calculations for simplifications or approximations when using square roots.