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1/16/ : Coordinates in 3 Dimensions 6.4: Coordinates in Three Dimensions Expectations: G1.1.5: Given a segment in terms of its endpoints, determine.

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1/16/20146.4: Coordinates in 3 Dimensions 6.4: Coordinates in Three Dimensions

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What is the sum of the 2 real solutions to the equation x = 6 – x 2 ? a. 6 b. 2 c. 1 d. -1 e. -6

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1/16/20146.4: Coordinates in 3 Dimensions Three Dimensional Coordinates 1. x-axis, y-axis, z-axis. 2. (x,y,z) ordered triples.

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1/16/20146.4: Coordinates in 3 Dimensions 3 Dimensional Coordinate System x y z

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1/16/20146.4: Coordinates in 3 Dimensions Plot (3,2,5)

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1/16/20146.4: Coordinates in 3 Dimensions Plot (-4,-1,2)

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1/16/20146.4: Coordinates in 3 Dimensions Plot (0,5,-4)

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1/16/20146.4: Coordinates in 3 Dimensions Coordinate Planes There are 3 coordinate planes in a 3 dimensional coordinate system. They are the xy plane, the yz plane and the xz plane. In the xy plane, the z coordinate of all points is 0. In the yz plane the x coordinate of all points is 0. In the xz plane the y coordinate of all points is 0.

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1/16/20146.4: Coordinates in 3 Dimensions Octants The xy, yz and xz planes split space into 8 regions called octants. The only octant that has a specific name is the region in which all 3 coordinates are positive. This octant is called the first octant.

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1/16/20146.4: Coordinates in 3 Dimensions Octants The other 7 octants are called out by location i.e. top back right or bottom front left.

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1/16/20146.4: Coordinates in 3 Dimensions Give the location (octant) of: (-4,9,8) Back, right, top (3,9,0) xy plane (-4, -8,-1) Back, left, bottom

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1/16/20146.4: Coordinates in 3 Dimensions Give the coordinates of a point: In the bottom back right octant. In the top front left octant In the xz coordinate plane.

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1/16/20146.4: Coordinates in 3 Dimensions Distance Formula in Three Dimensions The distance d between the points (x 1,y 1,z 1 ) and (x 2,y 2,z 2 ) is given by d=

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1/16/20146.4: Coordinates in 3 Dimensions Calculate the distance between (3,6,9) and (2,4,-8).

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Give the coordinates of 2 points that are 10 units apart in the 3-d coordinate system.

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1/16/20146.4: Coordinates in 3 Dimensions 3-D Midpoint Formula If A(x 1,y 1,z 1 ) and B(x 2,y 2,z 2 ), then the coordinates of the midpoint, M, of AB are given by the formula: M = x 1 +x 2, y 1 +y 2, z 1 +z 2 222

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1/16/20146.4: Coordinates in 3 Dimensions What are the coordinates of the midpoint of the segment determined by (-2,4,3) and (8, 12,-9)?

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1/16/20146.4: Coordinates in 3 Dimensions Assignment pages 399-400, # 14 - 48(evens)

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