Correct Option (A)
The scenario describes a three-dimensional geometric problem. Point P, where two walls and a ceiling meet at right angles, can be considered the origin (0,0,0) of a Cartesian coordinate system. The fly's position in the air can be represented by coordinates (x, y, z).
- The distance of the fly from one wall is 1 m. This can be assigned to the x-coordinate, so x = 1 m.
- The distance of the fly from the other wall is 8 m. This can be assigned to the y-coordinate, so y = 8 m.
- The distance of the fly from point P is 9 m. This is the space diagonal from the origin to the fly's position, calculated using the 3D distance formula: √(x² + y² + z²).
- The distance of the fly from the ceiling is the remaining coordinate, z.
Applying the 3D distance formula:
x² + y² + z² = (Distance from P)²
1² + 8² + z² = 9²
1 + 64 + z² = 81
65 + z² = 81
z² = 81 − 65
z² = 16
z = 4 (Since distance must be a positive value)
Therefore, the fly is 4 meters from the ceiling.
Incorrect Options:
Options B (6), C (12), and D (15) are incorrect. Substituting any of these values for 'z' in the 3D distance equation (1² + 8² + z² = 9²) would not satisfy the given condition that the fly is 9 meters from point P. For instance, if z=6, then 1² + 8² + 6² = 1 + 64 + 36 = 101, which is not equal to 9² (81).