1. 6.4: Coordinates in Three Dimensions
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6.4: Coordinates in 3 Dimensions

2. What is the sum of the 2 real solutions to the equation x = 6 – x2?1 -1 -6

3. Three Dimensional Coordinates
x-axis, y-axis, z-axis.
(x,y,z) ordered triples.
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6.4: Coordinates in 3 Dimensions

4. 3 Dimensional Coordinate Systemz y x
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6.4: Coordinates in 3 Dimensions

5. 6.4: Coordinates in 3 Dimensions
Plot (3,2,5)
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6.4: Coordinates in 3 Dimensions

6. 6.4: Coordinates in 3 Dimensions
Plot (-4,-1,2)
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6.4: Coordinates in 3 Dimensions

7. 6.4: Coordinates in 3 Dimensions
Plot (0,5,-4)
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6.4: Coordinates in 3 Dimensions

8. 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.
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6.4: Coordinates in 3 Dimensions

9. 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.
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6.4: Coordinates in 3 Dimensions

10. 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.
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6.4: Coordinates in 3 Dimensions

11. 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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6.4: Coordinates in 3 Dimensions

12. 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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6.4: Coordinates in 3 Dimensions

13. Distance Formula in Three Dimensions
The distance d between the points (x1,y1,z1) and (x2,y2,z2) is given by d=
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6.4: Coordinates in 3 Dimensions

14. 6.4: Coordinates in 3 Dimensions
Calculate the distance between (3,6,9) and (2,4,-8).
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6.4: Coordinates in 3 Dimensions

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

16. 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
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6.4: Coordinates in 3 Dimensions

17. 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)?
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6.4: Coordinates in 3 Dimensions

19. 6.4: Coordinates in 3 Dimensions
Assignment
pages ,
# (evens)
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6.4: Coordinates in 3 Dimensions