To convert this Cartesian coordinate into a polar coordinate #(r, theta)#, you need to find #r#, the distance of the point from the origin, and #theta#, the angle.
You can use the following formulas:
#r^2=x^2+y^2#
#tan theta = y/x#
#r^2=(-4)^2+0^2#
#r^2=16#
#r=4#
#tan theta = 0/-4#
#tan theta = 0#
#theta = tan^-1(0)#
#theta = 0#
Although the angle we obtained is #0#, the polar coordinate #(4,0)# does not make sense. This is because we used the #arctan# function, which only accounts for angles in the range #[-pi/2, pi/2]#. In order to get the correct angle, add #pi# to #0#. We now find that #theta=pi#.
So, the polar coordinate is #(4, pi)#. Plotting this coordinate shows that it is in the same location as the Cartesian coordinate #(-4, 0)#. The answer is #C#.
