What is the distance between (3 ,( pi)/4 ) and (-2 , ( pi )/2 )?

1 Answer
Feb 5, 2017

D=+-sqrt(13+6sqrt(2)) or D~~+-4.64

Explanation:

You are given two points in polar coordinates

  • (3,pi"/"4) where r_1=3 and theta_1=pi"/"4
  • (-2,pi"/"2) where r_2=-2 and theta_2=pi"/"2

The distance formula for polar coordinates is

D^2=r_1^2+r_2^2-2*r_1*r_2*cos(theta_2-theta_1)

Plug in the values above

D^2=3^2+(-2)^2-2(3)(-2)cos(pi"/"2-pi"/"4)
D^2=9+4+12cos(pi"/"4)
D^2=13+12(sqrt(2)/2)
D^2=13+6sqrt(2)

Now take the square root of both sides

D=+-sqrt(13+6sqrt(2))
D~~+-4.64