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This problem trains for: SAT-I, AMC-8, SAT-II.

In a cube of side 2 units what is the shortest distance between points A and B?

figure

figure

Drop a perpendicular from B onto MN and denote its 'foot' with C.

AB is the hypotenuse of right angle triangle ABC.

The leg BC is congruent to the side of the cube. Therefore, it has length 2 units.

The leg AC is the hypotenuse of the right triangle AMC and we can compute its length using the Pythagorean theorem:

equation

Use the Pythagorean theorem again in triangle ABC to get AB:

equation