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Question

# Name the octants in which the following points lie: (i) (5, 2, 3) (ii) (–5, 4, 3) (iii) (4, –3, 5) (iv) 7, 4, –3) (v) (–5, –4, 7) (vi) (–5, –3, –2) (vii) (2, –5, –7) (viii) (–7, 2 – 5)

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Solution

## (i) The x-coordinate, the y-coordinate and the z-coordinate of the point (5, 2, 3) are all positive. Therefore, this point lies in XOYZ octant. (ii) The x-coordinate, the y-coordinate and the z-coordinate of the point (−5, 4, 3) are negative, positive and positive, respectively. Therefore, this point lies in X'OYZ octant. (iii) The x-coordinate, the y-coordinate and the z-coordinate of the point (4, −3, 5) are positive, negative and positive, respectively. Therefore, this point lies in XOY'Z octant. (iv) The x-coordinate, the y-coordinate and the z-coordinate of the point (7, 4, −3) are positive, positive and negative, respectively. Therefore, this point lies in XOYZ' octant. (v) The x-coordinate, the y-coordinate and the z-coordinate of the point (−5, −4, 7) are negative, negative and positive, respectively. Therefore, this point lies in X'OY'Z octant . (vi) The x-coordinate, the y-coordinate and the z-coordinate of the point (−5, −3, −2) are all negative. Therefore, this point lies in X'OY'Z' octant (vii) The x-coordinate, the y-coordinate and the z-coordinate of the point (2, −5, −7) are positive, negative and negative, respectively. Therefore, this point lies in XOY'Z' octant. (viii) The x-coordinate, the y-coordinate and the z-coordinate of the point(−7, 2, −5) are negative, positive and negative, respectively. Therefore, this point lies in X'OYZ' octant.

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