What is the distance between $(4, \frac{7 π}{8})$ $(4 ,( 7 pi)/8 )$ and $(- 1, \frac{3 π}{2})$ $(-1 ,( 3pi )/2 )$ ?

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What is the distance between $(4, \frac{7 π}{8})$ $(4 ,( 7 pi)/8 )$ and $(- 1, \frac{3 π}{2})$ $(-1 ,( 3pi )/2 )$ ?

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Answer 1 · 2016-07-12T22:12:22

The distance is $\frac{5 \sqrt{16 + π^{2}}}{4}$ $(5sqrt(16 + pi^2))/4$

Explanation:

Distance between two points is the length of the vector between them. That is, for two points $\to A$ $vecA$ and $\to B$ $vecB$ , the distance will be: $∣ ∣ ∣ ∣ ∣ ∣ \to A - \to B ∣ ∣ ∣ ∣ ∣ ∣$ $||vecA - vecB||$ .

This means that for your points:
$d = \sqrt{{(4 + 1)}^{2} + {(\frac{7 π}{8} - \frac{3 π}{2})}^{2}}$ $d = sqrt((4+1)^2 + ((7pi)/8 - (3pi)/2)^2)$
$= \sqrt{5^{2} + {(\frac{- 5 π}{8})}^{2}}$ $= sqrt(5^2 + ((-5pi)/8)^2)$
$= \sqrt{25 + \frac{25 π^{2}}{16}} = \sqrt{\frac{400 + 25 π^{2}}{16}}$ $= sqrt(25 + (25pi^2)/16) = sqrt((400 + 25pi^2)/16)$
$= \frac{\sqrt{400 + 25 π^{2}}}{4} = \frac{5 \sqrt{16 + π^{2}}}{4}$ $= sqrt(400 + 25pi^2)/4 = (5sqrt(16 + pi^2))/4$

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What is the distance between $(4, \frac{7 π}{8})$ $(4 ,( 7 pi)/8 )$ and $(- 1, \frac{3 π}{2})$ $(-1 ,( 3pi )/2 )$ ?

1 Answer

Explanation:

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What is the distance between (4,7π8)(4 ,( 7 pi)/8 ) and (−1,3π2)(-1 ,( 3pi )/2 )?

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What is the distance between $(4, \frac{7 π}{8})$ $(4 ,( 7 pi)/8 )$ and $(- 1, \frac{3 π}{2})$ $(-1 ,( 3pi )/2 )$ ?