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Question

# How many of these are correctly matched ? Coordinates of a point Name of the octant 1. (1,2,3) P.I 2. (4,−2,3) Q.IV 3. (4,−2,−5) R.VIII 4. (4,2,−5) S.V 5. (−4,2,−5) T.VI 6. (−4,2,5) U.II 7. (−3,−1,6) V.III 8. (2,−4,−7) W.VIII ___

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Solution

## The sign of the coordinates of a point determine the octant in which the points lies. The following table shows the signs of the coordinates in eight octants. octantcoordinatesIIIIIIIVVVIVIIVIIIx+--++--+y++--++--z++++---- Now we can observe the given coordinates and find the correct octant for those coordinates. Point (1,2,3) ≡ (+,+,+) lies in I octant Point (4,−2,3) ≡ (+,−,+) lies in IV octant Point (4,−2,−5) ≡ (+,−,−) lies in VIII octant Point (4,2,−5) ≡ (+,+,−) lies in V octant Point (−4,2,−5) ≡ (−,+,−) lies in VI octant Point (−4,2,5) ≡ (−,+,+) lies in II octant Point (−3,−1,6) ≡ (−,−,+) lies in III octant Point (2,−4,−7) ≡ (+,−,−) lies in VIII octant All of them are matched correct.

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