Question

Which set of polar coordinates names the same point as () -5.1 ? O A. (5, 7 4 O B. 57 5, 4 37 O c. (5, IT D. 5,

Answer 1

Recall that the point (x,θ) (in polar coordinates) represents the same point as the following polar coordinates:

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

represents the same point as the point

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

Answer: Option B.