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To find the distance between points \( A(1, 2, 3) \) and \( B(4, 6, 8) \), we use the distance formula in 3D:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]

Substituting the coordinates of \( A \) and \( B \):

1. \( x_1 = 1 \), \( y_1 = 2 \), \( z_1 = 3 \)
2. \( x_2 = 4 \), \( y_2 = 6 \), \( z_2 = 8 \)

Calculating each term inside the square root:

\[
(x_2 - x_1)^2 = (4 - 1)^2 = 3^2 = 9
\]
\[
(y_2 - y_1)^2 = (6 - 2)^2 = 4^2 = 16
\]
\[
(z_2 - z_1)^2 = (8 - 3)^2 = 5^2 = 25
\]

Adding these results:

\[
d = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2}
\]

The correct answer is **(b) 5**.

Would you like a detailed explanation of each calculation step, or have any other questions?

Here are 5 related questions to further practice:

1. What is the distance between points \( C(2, -1, 5) \) and \( D(-3, 4, 7) \)?
2. How do you calculate distance between two points in 2D instead of 3D?
3. What is the distance between points if they have the same coordinates?
4. Can the distance formula be used for points in four-dimensional space?
5. How would you find the midpoint between two points in 3D?

**Tip:** For finding distances, always check the units (like in real-world applications) and confirm each squared difference before summing them up!

What is the distance between the points A(1,2,3) and B(4,6,8)?

Learn how to find the distance between points A(1,2,3) and B(4,6,8) using the 3D distance formula. This solution explains each step, making it suitable for students in Grades 9-12 studying geometry and spatial measurements.

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