The point which has polar coordinate (7, Pi/5) is reflected about the y-axis. What are the coordinate of the reflection?
A)(7,4pi/5)
B)(7,6pi/5)
C)(7,9pi/5)
D)(-7,pi/5)
E)(-7,6pi/5)

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \left(7,\frac{\mathrm{\pi }}{5}\right) \\ \mathrm{Now} 7 \mathrm{denotes} \mathrm{distance} \mathrm{from} \mathrm{origin} \mathrm{and} \frac{\mathrm{\pi }}{5} \mathrm{is} \mathrm{angle} \mathrm{made} \mathrm{with} \mathrm{X}-\mathrm{axis} \mathrm{in} \\ \mathrm{counter} \mathrm{clockwise} \mathrm{direction}. \\ \mathrm{As} \frac{\mathrm{\pi }}{5}<\frac{\mathrm{\pi }}{2}, \mathrm{hence} \left(7,\frac{\mathrm{\pi }}{5}\right) \mathrm{will} \mathrm{lie} \mathrm{in} \mathrm{first} \mathrm{quadrant}. \\ \mathrm{Now} \mathrm{if} \mathrm{rotate} \mathrm{point} \mathrm{about} \mathrm{Y}-\mathrm{axis} \mathrm{then} \mathrm{distance} \mathrm{from} \mathrm{origin} \mathrm{will} \mathrm{remain} \mathrm{same} \\ \mathrm{and} \mathrm{angle} \mathrm{will} \mathrm{be} \\ \mathrm{\theta }=\mathrm{\pi }-\frac{\mathrm{\pi }}{5}=\frac{4\mathrm{\pi }}{5} \\ \mathrm{Hence} \mathrm{new} \mathrm{co}-\mathrm{ordinates} \mathrm{will} \mathrm{be} \left(7,\frac{4\mathrm{\pi }}{5}\right) \\ \mathbf{Hence}\mathbf{ }\mathbf{option}\left(\mathbf{A}\right)\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{correct}\mathbf{.} \end{gathered}$$

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