What is the distance between $(2, \frac{3 π}{4})$ $(2 , (3 pi)/4 )$ and $(- 1, π)$ $(-1 , pi )$ ?

Question

2472 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-30T07:51:03

$\sqrt{5 + 2 \sqrt{2}}$ $sqrt(5+2sqrt(2))$

The polar point $(- 1, π)$ $(-1, pi)$ is equivalent to the polar point $(1, 0)$ $(1, 0)$ .

We can use the Law of Cosines to find the distance between the two points. Call the distance $c$ $c$ , we have:

$c = \sqrt{2^{2} + 1^{2} - 2 (2) (1) cos (\frac{3 π}{4})}$ $c = sqrt(2^2+1^2-2(2)(1)cos((3pi)/4))$

$= \sqrt{4 + 1 - 4 (- \frac{\sqrt{2}}{2})}$ $= sqrt(4+1-4(-sqrt(2)/2))$

$= \sqrt{5 + 2 \sqrt{2}}$ $= sqrt(5+2sqrt(2))$

What is the distance between (2 , (3 pi)/4 )(2,3π4)(2 , (3 pi)/4 ) and (-1 , pi )(−1,π)(-1 , pi )?