# What is the distance between the following polar coordinates?:  (1,-pi), (1,pi)

Jan 16, 2018

They are same point, so the distance between them is $0$.

#### Explanation:

Polar coordinates of point A is ${r}_{1} = 1.0 , {\theta}_{1} = - {180}^{0}$

Polar coordinates of point B is ${r}_{2} = 1.0 , {\theta}_{2} = {180}^{0}$

Cartesian coordinates of point A is ${x}_{1} = {r}_{1} \cos {\theta}_{1}$

or ${x}_{1} = 1.0 \cos \left(- 180\right) = - 1 , {y}_{1} = {r}_{1} \sin \theta$ or

${y}_{1} = 1 \sin 180 = 0 \therefore$ Cartesian coordinates of

point A is $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left(- 1 , 0\right)$

Cartesian coordinates of point B is ${x}_{2} = {r}_{2} \cos {\theta}_{2}$

or ${x}_{2} = 1.0 \cos 180 = - 1.0 , {y}_{2} = {r}_{2} \sin {\theta}_{2}$ or

${y}_{2} = 1.0 \sin 180 = 0$. Cartesian coordinates of

point B is $\left({x}_{2} , {y}_{2}\right) \mathmr{and} \left(- 1.0 , 0\right)$ . They are same point,

so the distance between them is $0$. [Ans]