1/16/20146.4: coordinates in 3 dimensions 6.4: coordinates in three dimensions
TRANSCRIPT
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04/10/23 6.4: 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 –
x2?
a. 6b. 2c. 1d. -1e. -6
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04/10/23 6.4: Coordinates in 3 Dimensions
Three Dimensional Coordinates
1. x-axis, y-axis, z-axis.2. (x,y,z) ordered triples.
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04/10/23 6.4: Coordinates in 3 Dimensions
3 Dimensional Coordinate System
x
y
z
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04/10/23 6.4: Coordinates in 3 Dimensions
Plot (3,2,5)
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04/10/23 6.4: Coordinates in 3 Dimensions
Plot (-4,-1,2)
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04/10/23 6.4: Coordinates in 3 Dimensions
Plot (0,5,-4)
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04/10/23 6.4: Coordinates in 3 Dimensions
Coordinate PlanesThere 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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04/10/23 6.4: Coordinates in 3 Dimensions
OctantsThe 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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04/10/23 6.4: Coordinates in 3 Dimensions
OctantsThe other 7 octants are called
out by location i.e. top back right or bottom front left.
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04/10/23 6.4: 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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04/10/23 6.4: 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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04/10/23 6.4: Coordinates in 3 Dimensions
Distance Formula in Three Dimensions
The distance d between the points (x1,y1,z1) and (x2,y2,z2) is given by
d=
2)1
z2
(z2)1
y2
(y2)1
x2
(x
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04/10/23 6.4: 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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04/10/23 6.4: Coordinates in 3 Dimensions
3-D Midpoint FormulaIf 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 2 2
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04/10/23 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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04/10/23 6.4: Coordinates in 3 Dimensions
Assignment pages 399-400, # 14 - 48(evens)