What is the distance between these points ?

Question

points are : ( 1/2, -5/3) ( -3/2, -2/3) 

 

When I try to solve I get a really long decimal number. The correct answer is √193/(6)

 

Please show me steps. Thank you 

Answer 1

 

The distance between the two points is defined as follows:

 

d = [ ( (-3/2) - (1/2) )^2 + ( (-2/3) - (-5/3) )^2 ]^(1/2) =

 

   =  [ (-4/2)^2 + (3/3)^2 ]^(1/2) = [2^2 + 1^2]^(1/2) =

  

   = 5^(1/2) 

 

That is, the distance between the two points is equal to the square 

root of 5.

This is an example of what is called an irrational number, a number that

cannot be precisely stated by any finite sequence of decimals.

By adding more and more decimals you get closer and closer to the exact

value, but you never get exactly there !

The wonders of math.

 

If you need help, I'm a tutor in the area of Westwood/Beverly Hills.