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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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**6.4: Coordinates in Three Dimensions**

3/25/2017 6.4: Coordinates in 3 Dimensions

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**What is the sum of the 2 real solutions to the equation x = 6 – x2?**

1 -1 -6

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**Three Dimensional Coordinates**

x-axis, y-axis, z-axis. (x,y,z) ordered triples. 3/25/2017 6.4: Coordinates in 3 Dimensions

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**3 Dimensional Coordinate System**

z y x 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Plot (3,2,5) 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Plot (-4,-1,2) 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Plot (0,5,-4) 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: 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. 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: 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. 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Octants The other 7 octants are called out by location i.e. top back right or bottom front left. 3/25/2017 6.4: Coordinates in 3 Dimensions

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**Give the location (octant) of:**

(-4,9,8) Back, right, top (3,9,0) xy plane (-4, -8,-1) Back, left, bottom 3/25/2017 6.4: Coordinates in 3 Dimensions

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**Give the coordinates of a point:**

In the bottom back right octant. In the top front left octant In the xz coordinate plane. 3/25/2017 6.4: Coordinates in 3 Dimensions

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**Distance Formula in Three Dimensions**

The distance d between the points (x1,y1,z1) and (x2,y2,z2) is given by d= 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Calculate the distance between (3,6,9) and (2,4,-8). 3/25/2017 6.4: Coordinates in 3 Dimensions

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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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**6.4: Coordinates in 3 Dimensions**

3-D Midpoint Formula If A(x1,y1,z1) and B(x2,y2,z2), then the coordinates of the midpoint, M, of AB are given by the formula: M = x1+x2 , y1+y2 , z1+z2 2 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

What are the coordinates of the midpoint of the segment determined by (-2,4,3) and (8, 12,-9)? 3/25/2017 6.4: Coordinates in 3 Dimensions

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**6.4: Coordinates in 3 Dimensions**

Assignment pages , # (evens) 3/25/2017 6.4: Coordinates in 3 Dimensions

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