Math 22 The Three-Dimensional Coordinate System

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The Three-Dimensional Coordinate System

3d spaces.png

The Distance and Midpoint Formulas

 The distance  between the points  and  is
 
 

Exercises 1 Find the distance between two points

1) and

Solution:  

2) and

Solution:  

Midpoint Formula in Space

 The midpoint of the line segment joining the points  and  is
 
 

Exercises 2 Find the midpoint of two points below:

1) and

Solution:  

2) and

Solution:  

Standard Equation of a Sphere

 The standard equation of a sphere with center at  and radius  is:
 
 

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