Question

Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with r<0 and the other with r>0 .(-5,0)

Answer 1

The point with polar coordinates (-5,0) is equivalent to (5, 180°) in standard polar coordinates. Other representations include (5, 360°) with r > 0 and (-5, 180°) with r < 0.

Step-by-step explanation:

To plot the point with the given polar coordinates (-5,0), we would normally locate the angle of 0 degrees from the positive x-axis and move along the line at that angle by the radial distance of 5 units. However, since the radial distance r is negative, we move in the opposite direction along the angle line, placing the point at (5, 180°) in standard polar coordinates. This corresponds to the point (5,0) in the Cartesian coordinate system.

For other representations with r > 0, we can add 360° to the angle to keep the same direction, giving us (5, 360°). For representations with r < 0, we can take the original point and add 180° to the angle, which flips the direction, giving us (-5, 180°).