Answer

To translate into polar coordinates we need to find the magnitude *r* and direction θ of the vector with the given components.This point, or vector, is in the third quadrant. The magnitude is

The direction is .

The polar coordinates are

These coordinates describe a point in the third quadrant, this is a reasonable answer.

This point is in the second quadrant. The magnitude is

The direction is .

The polar coordinates are

These coordinates still describe a point in the second quadrant, this is a reasonable answer.

This point is in the fourth quadrant. The magnitude is

The direction is .

The polar coordinates are

This describes a point in the fourth quadrant, this is a reasonable answer.

The point (0, -5) lies on the negative *y*-axis.We can see that its magnitude is 5 and its direction is 3π/2, its polar coordinates are .