3D Coordinate System

1
Section 8-6

• 3-D Coordinate System

2
3-D Coordinate System

• consists of three axes x, y and z
• 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)

z
y
x
3
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

4
Distance Formula

• the distance between two points

5
Midpoint Formula

• the midpoint of segment PQ with endpoints

6
Equation of a Sphere

• the equation of a sphere with radius of r and
  center at ( h , k , l )

7
Planes

• planes can be written as
• to sketch a plane, find and plot the three
  intercepts and then draw the triangle between
  them, add shading to give a 3D look