A student walks 1.0 kilometer due east and 1.0 kilometer due south. Then she runs 2.0  kilometers due west. The magnitude of the student's resultant displacement is closest to:

To find the magnitude of the resultant displacement, we can treat the student's movements as vectors and use vector addition. The displacement in the east direction is a vector of +1.0 kilometers, the displacement in the south direction is a vector of -1.0 kilometers, and the displacement in the west direction is a vector of -2.0 kilometers.
Now, let's add these vectors:
Resultant displacement in the east direction = +1.0 km Resultant displacement in the south direction = -1.0 km Resultant displacement in the west direction = -2.0 km
The resultant displacement vector, R, can be found by adding these vectors:
R = 1.0 km east - 1.0 km south - 2.0 km west
R = (1.0 km - 1.0 km - 2.0 km) = -2.0 km
The magnitude of the resultant displacement is the absolute value of this vector:
Magnitude of R = |-2.0 km| = 2.0 km
Therefore, the magnitude of the student's resultant displacement is closest to 2.0 kilometers.