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3.5 Graphs in Three Dimensions 1.Graphing Points in Three Dimensions 2.Graphing Equations in Three Dimensions

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Today…we enter…the third dimension… 1) Graphing Points in Three Dimensions Photos from: Street artist Julian Beever

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1) Graphing Points in Three Dimensions

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We live in a 3D world and need a third dimension to describe location Example: Name the three dimensions of the figure below.

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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.

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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…

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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

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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)

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

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

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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

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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

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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)

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

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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

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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

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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

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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)

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

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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)

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Homework (1)p.149 #1-12, 25 QUIZ: 3.1, 3.2 on WEDNESDAY

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