# What is the distance between the following polar coordinates?:  (3,(3pi)/4), (2,(7pi)/8)

Jul 4, 2017

$1.383$ $\text{units}$

#### Explanation:

We can do this by converting each coordinate to the equivalent Cartesian (rectangular) form, and using the distance formula:

$x = r \cos \theta$

$y = r \sin \theta$

${x}_{1} = 3 \cos \left(\frac{3 \pi}{4}\right) = - 2.121$

${y}_{1} = 3 \sin \left(\frac{3 \pi}{4}\right) = 2.121$

${x}_{2} = 2 \cos \left(\frac{7 \pi}{8}\right) = - 1.848$

${y}_{2} = 2 \sin \left(\frac{7 \pi}{8}\right) = 0.765$

$\text{distance} = \sqrt{{\left(- 2.121 - \left(- 1.848\right)\right)}^{2} + {\left(2.121 - 0.765\right)}^{2}}$

= color(blue)(1.383 color(blue)("units"