The rectangular coordinates of the point P are (-1,sqrt 3). If P is reflected witg respect to the x-axis, then the polar coordinates of its image are¡??

Question

The rectangular coordinates of the point P are (-1,sqrt 3). If P is reflected witg respect to the x-axis, then the polar coordinates of its image are¡­??

Reiny · Answer

(-1 , √3) ----> (-1 , -√3) after reflection in the x-axis
new point is in III,
tanØ = -√3/-1 = 240° in III
magnitude = √(1^2 + √3^2) = √4 = 2

point in polar coordinates:
(2cos240°, 2sin240°) or (2cos 4π/3, 2sin 4π/3)

The rectangular coordinates of the point P are (-1,sqrt 3). If P is reflected witg respect to the x-axis, then the polar coordinates of its image are¡­??

The rectangular coordinates of the point P are (-1,sqrt 3). If P is reflected witg respect to the x-axis, then the polar coordinates of its image are¡??