What is the distance between $(4, \frac{7 π}{6})$ $(4 ,( 7 pi)/6 )$ and $(3, \frac{- 3 π}{2})$ $(3 , ( -3 pi )/2 )$ ?

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What is the distance between $(4, \frac{7 π}{6})$ $(4 ,( 7 pi)/6 )$ and $(3, \frac{- 3 π}{2})$ $(3 , ( -3 pi )/2 )$ ?

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Answer 1 · 2017-10-03T21:54:16

$8.44$ $8.44$

Explanation:

Distance $= \sqrt{{(3 - 4)}^{2} + {((\frac{- 3 π}{2}) - (\frac{7 π}{6}))}^{2}}$ $=sqrt((3-4)^2+(((-3pi)/2)-((7pi)/6))^2$
$= \sqrt{1 + {(\frac{16 π}{6})}^{2}}$ $=sqrt(1+((16pi)/6)^2)$
$= \sqrt{1 + 70.18} = \sqrt{71.18} = 8.44$ $=sqrt(1+70.18)=sqrt71.18=8.44$ (as $π = \frac{22}{7}$ $pi=22/7$ )

Answer 2 · 2017-10-04T05:29:20

Distance between the two points is $4 \sqrt{3}$ $4sqrt3$

Explanation:

The polar coordinates $(4, \frac{7 π}{6})$ $(4,(7pi)/6)$ are equivalent to rectangular or Cartesian coordinates $(4 cos (\frac{7 π}{6}), 4 sin (\frac{7 π}{6}))$ $(4cos((7pi)/6),4sin((7pi)/6))$ i.e. $(- \frac{4 \sqrt{3}}{2}, - 2)$ $(-(4sqrt3)/2,-2)$ , and

polar coordinates $(3, - \frac{3 π}{2})$ $(3,-(3pi)/2)$ are equivalent to rectangular or Cartesian coordinates $(4 cos (- \frac{3 π}{2}), 4 sin (- \frac{3 π}{2}))$ $(4cos(-(3pi)/2),4sin(-(3pi)/2))$ i.e. $(0, 4)$ $(0,4)$

and distance between the two points is

$\sqrt{{(0 - (- \frac{4 \sqrt{3}}{2}))}^{2} + {(4 - (- 2))}^{2}}$ $sqrt((0-(-(4sqrt3)/2))^2+(4-(-2))^2)$

= $\sqrt{{(2 \sqrt{3})}^{2} + {(6)}^{2}}$ $sqrt((2sqrt3)^2+(6)^2)$

= $\sqrt{12 + 36} = \sqrt{48} = 4 \sqrt{3}$ $sqrt(12+36)=sqrt48=4sqrt3$

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What is the distance between $(4, \frac{7 π}{6})$ $(4 ,( 7 pi)/6 )$ and $(3, \frac{- 3 π}{2})$ $(3 , ( -3 pi )/2 )$ ?

2 Answers

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What is the distance between $(4, \frac{7 π}{6})$ $(4 ,( 7 pi)/6 )$ and $(3, \frac{- 3 π}{2})$ $(3 , ( -3 pi )/2 )$ ?