Question

What is the distance between `(4 ,( 7 pi)/8 )` and `(-1 ,( 3pi )/2 )`?

Answer 1

The distance is `(5sqrt(16 + pi^2))/4`

Explanation:

Distance between two points is the length of the vector between them. That is, for two points `vecA` and `vecB`, the distance will be: `||vecA - vecB||`.

This means that for your points:
`d = sqrt((4+1)^2 + ((7pi)/8 - (3pi)/2)^2)`
`= sqrt(5^2 + ((-5pi)/8)^2)`
`= sqrt(25 + (25pi^2)/16) = sqrt((400 + 25pi^2)/16)`
`= sqrt(400 + 25pi^2)/4 = (5sqrt(16 + pi^2))/4`