Question

What is the distance between `(4 ,( 7 pi)/6 )` and `(3 , ( -3 pi )/2 )`?

Answer 1

`8.44`

Explanation:

Distance `=sqrt((3-4)^2+(((-3pi)/2)-((7pi)/6))^2`
`=sqrt(1+((16pi)/6)^2)`
`=sqrt(1+70.18)=sqrt71.18=8.44` (as `pi=22/7`)

Answer 2

Distance between the two points is `4sqrt3`

Explanation:

The polar coordinates `(4,(7pi)/6)` are equivalent to rectangular or Cartesian coordinates `(4cos((7pi)/6),4sin((7pi)/6))` i.e. `(-(4sqrt3)/2,-2)`, and

polar coordinates `(3,-(3pi)/2)` are equivalent to rectangular or Cartesian coordinates `(4cos(-(3pi)/2),4sin(-(3pi)/2))` i.e. `(0,4)`

and distance between the two points is

`sqrt((0-(-(4sqrt3)/2))^2+(4-(-2))^2)`

= `sqrt((2sqrt3)^2+(6)^2)`

= `sqrt(12+36)=sqrt48=4sqrt3`