1. 3.5 Graphs in Three Dimensions
Graphing Points in Three Dimensions
Graphing Equations in Three Dimensions

2. 1) Graphing Points in Three Dimensions
We live in a 3D world and need a “third dimension” to describe location
Example:
Name the three dimensions of the figure below.

3. 1) Graphing Points in Three Dimensions
We live in a 3D world and need a “third dimension” to describe location
Example:
Name the three dimensions of the figure below.
Answer:
The figure has length, width and
height.

4. 1) Graphing Points in Three Dimensions
The x-axis describes horizontal movement
The y-axis describes vertical movement
The z-axis describes movement somewhere in between…

5. 1) Graphing Points in Three Dimensions
How to graph in 3-dimensions…
x – shift forward and backward
y – shift left and right
z – shift up and down

6. 1) Graphing Points in Three Dimensions
How to graph in 3-dimensions…
x – shift forward and backward
y – shift left and right
z – shift up and down
Points are communicated as (x, y, z)

7. 1) Graphing Points in Three Dimensions
Example 1:
Graph (0, 3, -2).

8. 1) Graphing Points in Three Dimensions
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement x -x y -y z -z

9. 1) Graphing Points in Three Dimensions
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units x -x y -y z -z

10. 1) Graphing Points in Three Dimensions
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units
z = -2; move down 2 units x -x y -y z -z

11. 1) Graphing Points in Three Dimensions
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units
z = -2; move down 2 units x -x y -y z -z

12. 1) Graphing Points in Three Dimensions
Example 2:
Graph (-3, 3, -4).

13. 1) Graphing Points in Three Dimensions
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units x -x y -y z -z

14. 1) Graphing Points in Three Dimensions
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units
y = 3; move right 3 units x -x y -y z -z

15. 1) Graphing Points in Three Dimensions
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units
y = 3; move right 3 units
z = -4; move down 4 units x -x y -y z -z

16. 1) Graphing Points in Three Dimensions
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units
y = 3; move right 3 units
z = -4; move down 4 units x -x y -y z -z

17. 1) Graphing Points in Three Dimensions
Example 3:
Find the coordinates of the point below. x -x y -y z -z

18. 1) Graphing Points in Three Dimensions
Example 3:
Find the coordinates of the point below. x -x y -y z -z

19. 1) Graphing Points in Three Dimensions
Example 3:
Find the coordinates of the point below.
Therefore,
the solution
is (2, -3, 3) x -x y -y z -z

20. Homework
p.149 #3, 4, 6, 7, 8
Worksheet:
Points in Three Dimensions