**A point is on the x-axis. What are its y-coordinates and z-coordinates?**

Solution:

If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.

**A point is in the XZ-plane. What can you say about its y-coordinate?**

Solution:

If a point is in the XZ plane, then its y-coordinate is zero.

**Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)**

Solution:

The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive.

Therefore, this point lies in octant I.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.

The x-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.

The x-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII

**Fill in the blanks:**

**(i) The x-axis and y-axis taken together determine a plane known as_______.**

**(ii) The coordinates of points in the XY-plane are of the form _______.**

**(iii) Coordinate planes divide the space into ______ octants.**

Solution:

(i) xy-plane

(ii) (x, y, 0)

(iii) eight

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