Distance Math Example 4

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Example 4

hard
Find the distance between points A(1,2,3)A(1, 2, 3) and B(4,6,3)B(4, 6, 3) in 3D space.

Solution

  1. 1
    Step 1: The 3D distance formula is d=(x2−x1)2+(y2−y1)2+(z2−z1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.
  2. 2
    Step 2: d=(4−1)2+(6−2)2+(3−3)2=9+16+0=25=5d = \sqrt{(4-1)^2+(6-2)^2+(3-3)^2} = \sqrt{9+16+0} = \sqrt{25} = 5.

Answer

d=5d = 5 units
The 3D distance formula is a natural extension of the 2D version using the Pythagorean theorem in three dimensions. Since the z-coordinates are equal here, the distance reduces to a 2D calculation. This formula generalises to nn dimensions.

About Distance

The length of the shortest path between two points, always a non-negative real number.

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More Distance Examples

Example 1 easy

Find the distance between points [formula] and [formula].

Example 2 medium

Find the distance between [formula] and [formula]. Leave your answer in simplest radical form.

Example 3 easy

What is the distance from the origin [formula] to the point [formula]?

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