Distance Formula

Question

The distance between points (1, 2, 3) and (4, 6, 8) is

RankGuru · Accepted Answer

1. **Formula**: The distance $d$ between points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is:
   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$
2. **Calculation**: Using $(1, 2, 3)$ and $(4, 6, 8)$:
   $d = \sqrt{(4-1)^2 + (6-2)^2 + (8-3)^2}$
   $d = \sqrt{(3)^2 + (4)^2 + (5)^2}$
   $d = \sqrt{9 + 16 + 25} = \sqrt{50}$
3. **Result**: The distance is $\sqrt{50}$ units (which is $5\sqrt{2}$).

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