Town W is 14 km West of Town X. Town Y is 12 km South of Town X. Town Z is 5 km North of Town W. What is the straight-line distance between Town Z and Town Y?
Answer and explanation
Correct answer: C. sqrt(485) km ≈ 22.02 km
- Step 1: Coordinate representation: X = (0, 0), W = (-14, 0), Y = (0, -12), Z = (-14, 5).
- Step 2: Vector ZY = (0 - (-14), -12 - 5) = (14, -17).
- Step 3: Distance = sqrt(14^2 + (-17)^2) = sqrt(196 + 289) = sqrt(485) ≈ 22.02 km.
Why not the others: The remaining options (sqrt(450) km ≈ 21.21 km, sqrt(505) km ≈ 22.47 km, sqrt(465) km ≈ 21.56 km) violate logical deduction rules, confuse necessary and sufficient conditions, or stem from calculation slips.
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