Question

Which set of polar coordinates names the same point as (-5.5) ? ZT O O A. (5, O B. (5:59) O 5 57 4 377 O c. -5 O D. 7T 5. )

Answer 1

Recall that the following points represent the same point as the point (x,θ)

`\begin{gathered} (-x,\theta+\pi), \\ (-x,\theta-\pi), \\ (x,\theta+2n\pi)\text{.} \end{gathered}`

Now, notice that:

`(5\pi)/(4)=(4\pi)/(4)+(\pi)/(4)=\pi+(\pi)/(4)\text{.}`

Therefore, the point:

`(5,(5\pi)/(4))`

represent the same point as the point

`(-5,(\pi)/(4))\text{.}`

Answer: Option B.