Transcript Section 8-6 3-D Coordinate System 3-D Coordinate System • consists of three axes – x, y and z z y x • points are denoted with.

Section 8-6
3-D Coordinate System
3-D Coordinate System
• consists of three axes – x, y and z
z
y
x
• points are denoted with an ordered triple
(x , y , z)
• x-int (x , 0 , 0) y-int (0 , y , 0) z-int (0 , 0 , z)
3-D Coordinate System
• there are three coordinate planes
– xy-plane equation z = 0
– xz-plane equation y = 0
– yz-plane equation x = 0
• the axes meet at the origin (0 , 0 , 0)
• space is divided into 8 regions called
octants
Distance Formula
• the distance between two points
P( x1 , y1 , z1 ) and Q(x2 , y2 , z2 )
d  ( x1  x2 )  ( y1  y2 )  ( z1  z2 )
2
2
2
Midpoint Formula
• the midpoint of segment PQ with endpoints
P( x1 , y1 , z1 ) and Q(x2 , y2 , z2 )
 x1  x2 y1  y2 z1  z2 
M 
,
,

2
2 
 2
Equation of a Sphere
• the equation of a sphere with radius of r
and center at ( h , k , l )
( x  h)  ( y  k )  ( z  l )  r
2
2
2
2
Planes
• planes can be written as:
Ax  By  Cz  D  0
• to sketch a plane, find and plot the three
intercepts and then draw the triangle
between them, add shading to give a 3D
look