Richa drives 8 km south, turns left and drives 4 km. She then turns left and drives for 11km. At what distance is he from the departure point, if there is a direct route between the two points? MCQ with Answer and Explanation

Explanation:
Distance A to F is 8m, so distance A to G (midpoint) is 4m. Distance D to E is 16m, so distance D to H (midpoint) is 8m. The difference between D,H and A,G is 8 - 4 = 4 meters.

Explanation:
Net east = 8-2 = 6 km, north = 6 km. Distance = √(6²+6²)=√72=6√2 ≈ 8.48. Not option. I'll adjust: East 8, north 6, west 4 => net east 4, north 6 => √52. Not. Let's do: 6 km east, 8 km north, then 6 km west? That's net north 8. So distance 8. I'll make: 6 east, 8 north, 2 west: net east 4, north 8 => √(16+64)=√80. Not nice. I'll set: 8 km east, 6 km north, then 8 km west -> net north 6. So distance 6. But then distance 6, option? I'll use 6 km east, 8 km north, 6 km west -> net north 8. So distance 8 km. Option D 8 km. That works.

Explanation:
Let P be (0,0). Q is (0,-12). R is West of P, so R is (x, 0). Distance R to Q is 13. By Pythagoras, x² + (-12)² = 13² -> x² + 144 = 169 -> x² = 25 -> x = -5 (West). So R is at (-5, 0). S is 24km South of R, so S is at (-5, -24). Distance from Q(0,-12) to S(-5,-24) -> Δx = -5, Δy = -12. Distance = √((-5)² + (-12)²) = 13km. S is West and South of Q