Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?
Answer & explanation
Answer: (a) 4
Take P as the corner where the three perpendicular surfaces meet. The fly's distances from the two walls and the ceiling are its three coordinates, so 1² + 8² + h² = 9², giving h² = 16 and h = 4 m.
- Take P as the origin, with the two walls and the ceiling as three mutually perpendicular planes.
- The distance from each plane is one coordinate: 1 m, 8 m and h m (from the ceiling).
- Distance from P: √(1² + 8² + h²) = 9, so 1 + 64 + h² = 81.
- h² = 16, so h = 4 m.
Remember · Distance from a corner = √(x² + y² + z²), where x, y and z are the distances from the three faces meeting there.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·