Ricky travels 5 km in a straight line from home (assume standard convention: initial heading North), then takes a right turn and goes 6 km, then takes a left turn and goes 3 km. What is his straight-line distance from home now?

Introduction / Context:
The original statement does not specify the first direction. Under the standard recovery convention for such items, we assume the first leg is due North. After that, a right turn leads to East, and a subsequent left brings the heading back to North. We must compute the net displacement.

Given Data / Assumptions:

• Assumed initial heading: North (5 km).
• Right turn → East (6 km).
• Left turn from East → North (3 km).
• Compute straight-line distance from home to the final point.

Concept / Approach:
Sum orthogonal components. North–South total: 5 + 3 = 8 km North. East–West total: 6 km East. Use the Pythagorean theorem for the resultant.

Step-by-Step Solution:

Verification / Alternative check:
The legs 6 and 8 form another well-known Pythagorean triple with hypotenuse 10.

Why Other Options Are Wrong:
9, 11, or 12 km do not satisfy the relation d^2 = 6^2 + 8^2 for orthogonal movement.

Common Pitfalls:
Assuming a different initial heading without stating it; the Recovery-First Policy permits the standard North assumption when unspecified.

Final Answer:
10 km