A person starts from point A, walks 6 km towards North to reach B, turns right and walks 8 km to reach C. What is the shortest distance between A and C?

Explanation

From A to B, the person moves 6 km north. Turning right from north means moving east, so B to C is an 8 km eastward leg. These two movements are perpendicular, making triangle ABC a right-angled triangle with AC as the straight-line distance. The NCERT Manual for Secondary Mathematics Kit states Pythagoras theorem for a right-angled triangle: the square of the hypotenuse equals the sum of the squares of the other two sides. Applying it here, AC = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 km.

Why the other options are wrong

• (B) 14 km is the total walking distance, AB plus BC, not the shortest straight-line distance from A to C.
• (C) 8 km is only the eastward leg from B to C, so it ignores the 6 km northward movement from A to B.
• (D) 12 km does not follow from Pythagoras theorem, because sqrt(6^2 + 8^2) equals 10, not 12.

Concept

This tests direction sense combined with Pythagoras theorem: after tracking turns, the shortest distance is the hypotenuse of a right-angled triangle. It recurs in RAS mental ability because such questions check both spatial tracking and quick numerical reasoning.

Source

• NCERT Manual for Secondary Mathematics Kit

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