Three Dimensional Geometry
Exercise 11.1 Solutions
Coordinate Signs in Octants:
I: $(+,+,+)$ II: $(-,+,+)$ III: $(-,-,+)$ IV: $(+,-,+)$
V: $(+,+,-)$ VI: $(-,+,-)$ VII: $(-,-,-)$ VIII: $(+,-,-)$
[Image of 3D coordinate system octants]
I: $(+,+,+)$ II: $(-,+,+)$ III: $(-,-,+)$ IV: $(+,-,+)$
V: $(+,+,-)$ VI: $(-,+,-)$ VII: $(-,-,-)$ VIII: $(+,-,-)$
Q1
1. A point is on the x-axis. What are its y-coordinate and z-coordinates?
Concept
Any point on the x-axis has coordinates of the form $(x, 0, 0)$.
y-coordinate = 0, z-coordinate = 0
Q2
2. A point is in the XZ-plane. What can you say about its y-coordinate?
Concept
The XZ-plane is defined by points where distance from it along the y-axis is zero. Coordinates are $(x, 0, z)$.
y-coordinate is 0
Q3
3. Name the octants in which the following points lie:
| Point | Signs | Octant |
|---|---|---|
| (1, 2, 3) | (+, +, +) | I |
| (4, -2, 3) | (+, -, +) | IV |
| (4, -2, -5) | (+, -, -) | VIII |
| (4, 2, -5) | (+, +, -) | V |
| (-4, 2, -5) | (-, +, -) | VI |
| (-4, 2, 5) | (-, +, +) | II |
| (-3, -1, 6) | (-, -, +) | III |
| (-2, -4, -7) | (-, -, -) | VII |
Q4
4. Fill in the blanks:
(i)
The x-axis and y-axis taken together determine a plane known as XY-plane.
(ii)
The coordinates of points in the XY-plane are of the form (x, y, 0).
(iii)
Coordinate planes divide the space into 8 (eight) octants.