Question

What is the distance between `(4 ,( 7 pi)/6 )` and `(-1 ,( 3pi )/2 )`?

Answer 1

The distance between the two points is `sqrt(3)` units

Explanation:

To find the distance between these two points, first convert them into regular coordinates. Now, if `(r,x)` are the coordinates in polar form, then the coordinates in regular form are `(rcosx,rsinx)`.
Take the first point `(4,(7pi)/6)`.
This becomes `(4cos((7pi)/6),4sin((7pi)/6))`

=`(-2sqrt(3),-2)`

The second point is `(-1,(3pi)/2)`
This becomes `(-1cos((3pi)/2),-1sin((3pi)/2))`

=`(0,1)`

So now the two points are `(-2sqrt(3),-2)` and `(0,1)`. Now we can use the distance formula
`d=sqrt((-2sqrt(3)-0)^2 - (-2-1)^2)`

=`sqrt(12-9)`

=`sqrt(3)`