3.5 graphs in three dimensions 1.graphing points in three dimensions 2.graphing equations in three...
TRANSCRIPT
![Page 1: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/1.jpg)
3.5 Graphs in Three Dimensions
1. Graphing Points in Three Dimensions
2. Graphing Equations in Three Dimensions
![Page 2: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/2.jpg)
Today…we enter…the third dimension…
1) Graphing Points in Three Dimensions
Photos from:
http://users.skynet.be/J.Beever/pave.htm
Street artist Julian Beever
![Page 3: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/3.jpg)
1) Graphing Points in Three Dimensions
![Page 4: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/4.jpg)
1) Graphing Points in Three Dimensions
![Page 5: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/5.jpg)
1) Graphing Points in Three Dimensions
![Page 6: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/6.jpg)
1) Graphing Points in Three Dimensions
![Page 7: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/7.jpg)
1) Graphing Points in Three Dimensions
![Page 8: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/8.jpg)
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.
![Page 9: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/9.jpg)
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.
![Page 10: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/10.jpg)
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…
![Page 11: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/11.jpg)
How to graph in 3-dimensions…
x – shift forward and backward
y – shift left and right
z – shift up and down
1) Graphing Points in Three Dimensions
![Page 12: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/12.jpg)
How to graph in 3-dimensions…
x – shift forward and backward
y – shift left and right
z – shift up and down
1) Graphing Points in Three Dimensions
Points are communicated as
(x, y, z)
![Page 13: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/13.jpg)
Example 1:
Graph (0, 3, -2).
1) Graphing Points in Three Dimensions
![Page 14: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/14.jpg)
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 15: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/15.jpg)
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 16: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/16.jpg)
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units
z = -2; move down 2 units
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 17: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/17.jpg)
Example 1:
Graph (0, 3, -2).
Answer:
x = 0; no movement
y = 3; move right 3 units
z = -2; move down 2 units
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
(0, 3, -2)
![Page 18: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/18.jpg)
Example 2:
Graph (-3, 3, -4).
1) Graphing Points in Three Dimensions
![Page 19: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/19.jpg)
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 20: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/20.jpg)
Example 2:
Graph (-3, 3, -4).
Answer:
x = -3; move backward 3 units
y = 3; move right 3 units
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 21: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/21.jpg)
x
-x
y
-y
z
-z
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
1) Graphing Points in Three Dimensions
![Page 22: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/22.jpg)
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
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
(-3, 3, -4)
![Page 23: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/23.jpg)
Example 3:
Find the coordinate of the point below.
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
![Page 24: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/24.jpg)
Example 3:
Find the coordinate of the point below.
Therefore,
the solution
is (2, -3, 3)
1) Graphing Points in Three Dimensions
x
-x
y
-y
z
-z
(2, -3, 3)
![Page 25: 3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions](https://reader036.vdocuments.net/reader036/viewer/2022081414/55143bbf5503462d4e8b46a1/html5/thumbnails/25.jpg)
Homework
(1) p.149 #1-12, 25
QUIZ: 3.1, 3.2 on WEDNESDAY