## EXERCISE 12.1

#### Page No 271:

#### Question 1:

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

#### Answer:

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

#### Question 2:

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

#### Answer:

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

#### Question 3:

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)

#### Answer:

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**.

#### Question 4:

Fill in the blanks:

#### Answer:

(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.