Reena walks from point A to point B, 10 feet towards the east. Then she turns to her right and walks 3 feet. Again she turns to her right and walks 14 feet. At this stage, how far is she from her original point A?

Introduction / Context:
This direction sense question involves Reena walking along a path that includes two right angle turns. The movements form a right angled shape on the ground. We are asked to determine the straight line distance between her final position and the starting point A. The underlying concept is basic right angled triangle geometry with short integer distances.

Given Data / Assumptions:

• Reena starts from point A.
• She walks 10 feet east to reach point B.
• From there, she turns right, faces south, and walks 3 feet.
• Again she turns right from facing south, so she faces west and walks 14 feet.
• We need the straight line distance from her final position back to A.

Concept / Approach:
We will model Reena's movements using coordinates. Treating east as positive x and north as positive y, each step can be described as a change in x and y. After summing these changes, we obtain her final coordinates. The distance between the starting point and final point is then found using the Pythagorean theorem, because the path forms a right angled triangle whose legs are the horizontal and vertical displacements.

Step-by-Step Solution:
Step 1: Place point A at (0, 0).Step 2: After walking 10 feet east, Reena is at (10, 0) and facing east.Step 3: She turns right, which from east means facing south, and walks 3 feet to reach (10, −3).Step 4: She turns right again, which from south means facing west, and walks 14 feet to reach (−4, −3).Step 5: Her final position is at (−4, −3) relative to A at (0, 0).Step 6: The horizontal displacement is 4 feet west, and the vertical displacement is 3 feet south.Step 7: The straight line distance d between A and her final position is d = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 feet.

Verification / Alternative check:
We can verify the calculations by noting that the 3, 4, 5 triangle is a well known Pythagorean triple. Any right angled triangle with legs 3 and 4 has a hypotenuse of 5. Since Reena ends up 4 feet west and 3 feet south of the starting point, the triangle formed by her final position, the foot of a perpendicular on the starting vertical line, and point A is such a 3, 4, 5 triangle. Therefore, the direct distance from A to her final position must be exactly 5 feet.

Why Other Options Are Wrong:
The option 4 feet corresponds only to the horizontal separation and ignores the vertical displacement. The value 24 feet is the sum of some of the segments and does not measure the crow flight distance. Similarly, 27 feet is the sum of all three legs of the path and represents the total walking distance, not the straight line distance from the start. The 14 feet option corresponds to one of the walking segments but has nothing to do with the final displacement from A.

Common Pitfalls:
Some students confuse total path length with straight line distance and therefore add the legs 10, 3, and 14. Others misinterpret the turns and draw the last segment incorrectly to the east instead of west. Clearly marking the directions after each turn and plotting the path as a simple figure on grid paper are effective strategies to avoid these mistakes.

Final Answer:
The straight line distance between Reena's final position and the starting point A is 5 feet.