3.5 Graphs in Three Dimensions

1. Graphing Points in Three Dimensions

2. Graphing Equations in Three Dimensions

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

1) Graphing Points in Three Dimensions

1) Graphing Points in Three Dimensions

1) Graphing Points in Three Dimensions

1) Graphing Points in Three Dimensions

1) Graphing Points in Three Dimensions

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.

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.

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…

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

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)

Example 1:

Graph (0, 3, -2).

1) Graphing Points in Three Dimensions

Example 1:

Graph (0, 3, -2).

Answer:

x = 0; no movement

1) Graphing Points in Three Dimensions

x

-x

y

-y

z

-z

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

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

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)

Example 2:

Graph (-3, 3, -4).

1) Graphing Points in Three Dimensions

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

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

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

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)

Example 3:

Find the coordinate of the point below.

1) Graphing Points in Three Dimensions

x

-x

y

-y

z

-z

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)

Homework

(1) p.149 #1-12, 25

QUIZ: 3.1, 3.2 on WEDNESDAY