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.