### Introduction to Three Dimensional Geometry Exercise 1

## Question:

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

## Answer:

Answer:

- The point is in the XZ-plane, so it has an x-coordinate and a z-coordinate.
- Since the point is in the XZ-plane, its y-coordinate must be equal to 0.

## Question:

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:

(1,2,3) - Octant I (4,-2,3) - Octant II (4,-2,-5) - Octant VII (4,2,-5) - Octant VIII (-4,2,-5) - Octant V (-4,2,5) - Octant IV (-3,-1,6) - Octant III (2,-4,-7) - Octant VI

## Question:

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

## Answer:

(i) The x-axis and y-axis taken together determine a plane known as the XY-plane.

(ii) The coordinates of points in the XY-plane are of the form (x, y).

(iii) Coordinate planes divide the space into four quadrants or eight octants.

## Question:

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

## Answer:

Answer: The y-coordinate of the point is 0 and the z-coordinate is also 0.