Question

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

Answer 1

`sqrt`13

Explanation:

(x, y) = (r cos `theta`, r sin `theta` ) are components of the position vector ( r, `theta` ).
The radial vectors are ( `-2` `sqrt`3, `-2` ) and ( 0, `-3` ). The vector between the given points is the difference (`-2` `sqrt`3, 1 ). .
The distance is the length of this vector = `sqrt`13.

Answer 2

`3.606`

Explanation:

Point `(4,(7pi)/6)` in Cartesian coordinates represents `(4cos(7pi)/6), 4sin(7pi)/6))`

i.e. `(4xx(-sqrt3/2), 4xx((-1)/2))` or `(-2sqrt3, -2)`

Point `(3,-(pi)/2)` in Cartesian coordinates represents `(3cos(-pi/2),3sin(-pi/2))`

i.e. `(3xx0, 3xx(-1))` or `(0, -3)`

Hence distance between `(-2sqrt3, -2)` and `(0,-3)`

is `sqrt((0-(-2sqrt3))^2+(-3-(-2))^2`

= `sqrt((2sqrt3)^2+(-1)^2`

= `sqrt(12+1)`

= `sqrt13` = `3.606`