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:
 
 

Exercises 3 Find the equation of the sphere that has:

1) Center: and radius:

Solution:  
So,
Therefore, Failed to parse (syntax error): {\displaystyle (x-1)^2+(y-2)^2+z^2=25 |} '''2)''' Center: <math>(-1,2,4)} and radius:
Solution:  
So,
Therefore, <math>(x+1)^2+(y-2)^2+(z-4)^2=4

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