What is the distance between $(4, \frac{5 π}{6})$ $(4 ,(5 pi)/6 )$ and $(- 1, \frac{19 π}{12})$ $(-1 , (19 pi )/12 )$ ?

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Answer 1 · 2018-06-30T21:47:06

$\approx 10.55$ $~~10.55$ units

We want to use the Distance Formula, which is really derived from the Pythagorean theorem.

Distance Formula

$sqrt((Deltax)^2+(Deltay)^2)$

Where $Delta$ is the Greek letter denoting "change in".

How much does our $x$ change by?

Well we go from $4$ to $-1$ , so this means

$color(blue)(Deltax=-5)$

How much does our $y$ change by?

$y$ starts out at $(10pi)/12$ , but goes to $(19pi)/12$ . We can say

$Deltay=(9pi)/12$ or $color(blue)(Deltay=(3pi)/4)$

Let's plug these into the distance formula to get

$sqrt((-5)^2+((3pi)/4)^2)$

This simplifies to

$5+9/16 pi^2$

Which is approximately

$5+5.55=10.55$ units

Hope this helps!

What is the distance between (4 ,(5 pi)/6 )(4,5π6)(4 ,(5 pi)/6 ) and (-1 , (19 pi )/12 )(−1,19π12)(-1 , (19 pi )/12 )?