Question

What is the distance between `(2 , (3 pi)/4 )` and `(-1 , pi )`?

Answer 1

`sqrt(5+2sqrt(2))`

Explanation:

The polar point `(-1, pi)` is equivalent to the polar point `(1, 0)`.

We can use the Law of Cosines to find the distance between the two points. Call the distance `c`, we have:

`c = sqrt(2^2+1^2-2(2)(1)cos((3pi)/4))`

`= sqrt(4+1-4(-sqrt(2)/2))`

`= sqrt(5+2sqrt(2))`