What is the distance between (5 ,( pi)/4 ) and (3 , (11 pi )/6 )?

Jun 24, 2018

$5.36$

Explanation:

To solve this, you need the distance formula between two points which is:

$D = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$

where the first point is $\left({x}_{1} , {y}_{1}\right)$

and the second point is $\left({x}_{2} , {y}_{2}\right)$.

It doesn't matter which point is the first point or second point. The difference will always be the same, and when you square the difference in the equation, the negative difference will go away.

E.g. Say ${x}_{1}$ is $117$ and ${x}_{2}$ is $100$.

$117 - 100 = 17$ and

$100 - 117 = - 17$

When you square the $17$ and $- 17$, they both yield the same answer: $289$.

Now plug in the two points from the problem.

$\left({x}_{1} , {y}_{1}\right) = \left(5 , \frac{\Pi}{4}\right)$

$\left({x}_{2} , {y}_{2}\right) = \left(3 , \frac{11 \Pi}{6}\right)$

$D = \sqrt{{\left(5 - 3\right)}^{2} + {\left(\frac{\Pi}{4} - \frac{11 \Pi}{6}\right)}^{2}}$

$D = \sqrt{{\left(2\right)}^{2} + {\left(- 4.974\right)}^{2}}$

$D = \sqrt{4 + 24.74}$

$D = \sqrt{28.74}$

$D = 5.36$