Reena walked 10 feet from point A to point B, towards the East. She then…

CONCEPT: In a direction-and-distance problem built from perpendicular legs (each 90° turn swaps the direction between East-West and North-South), the straight-line distance between the starting point and the final point equals the hypotenuse of a right triangle. The two legs of that triangle are the NET horizontal (East-West) displacement and the NET vertical (North-South) displacement, related by the Pythagorean theorem: distance2 = (horizontal leg)2 + (vertical leg)2.

1. Fix a coordinate system with A as the origin: take East as the positive x-direction and North as the positive y-direction.

2. Reena walks 10 feet East from A, so she reaches B = (10, 0).

3. Facing East, turning right means she now faces South. Walking 3 feet South takes her to C = (10, -3).

4. Facing South, turning right again means she now faces West. Walking 14 feet West takes her to D = (10 - 14, -3) = (-4, -3).

5. The net horizontal displacement from A is |-4| = 4 feet, and the net vertical displacement is |-3| = 3 feet.

6. By the Pythagorean theorem, AD = √(42 + 32) = √(16 + 9) = √25 = 5 feet.

CROSS-CHECK: 3, 4, 5 is the standard Pythagorean triple, since 32 + 42 = 9 + 16 = 25 = 52. So a right triangle with legs 3 feet and 4 feet must have a hypotenuse of exactly 5 feet, independently confirming the computed distance.

Hence, Reena is 5 feet away from A.