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

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

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Answer 1 · 2016-01-05T02:22:19

Sometimes the solution is as simple as just thinking about the problem :)

Explanation:

$(4, \frac{- 3 π}{4})$ $(4, (-3pi)/4)$ is in Quadrant III with a reference angle of $45^{o}$ $45^o$ and a radius of 4 .

$(- 2, \frac{π}{4})$ $(-2,pi/4)$ should be in Quadrant I, but the negative 2 flips it $180^{o}$ $180^o$ in Quadrant III with a radius of 2 and also with a reference angle of $45^{o}$ $45^o$

So, these two points lie on the same $θ = 45^{o}$ $theta=45^o$ in Quadrant IV with a distance between them equal to $4 - 2 = 2$ $4-2=2$

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

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Explanation:

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