Question

In a set of tracks, to go from A to B you must travel 100m to the west and 300m to the south. To go from B to C you must travel 200m east and 100m north. What should be the route to go directly from A to C?
A. 100m east and 200m south
B. 300m east and 200m south 
C. 300m east and 400m south 
D. 100m east and 400m south 
E. 300m west and 100m north 

Answer 1

Let coordinates of point A be (0 m, 0 m). Then, the person travels from point A to point B 100 meters to the west and 300 meters to the south. Therefore, the displacement along the axis $x$- and $y-$ will be:

$$\Delta x=x_f-x_i=-100\ m-0=-100 m,$$ $$\Delta y=y_f-y_i=-300\ m-0=-300 m.$$

Hence, the coordinates of point B is (-100 m, -300 m).

Then, the person travels from point B to point C 200 meters east and 100 meters north. Therefore, the displacement along the axis $x$- and $y-$ will be:

$$\Delta x=x_f-x_i=200\ m-100\ m=100\ m,$$ $$\Delta y=y_f-y_i=100\ m-300\ m=-200\ m.$$

Hence, the coordinates of point C is (100 m, -200 m).

As we can see, to go directly from point A to point C we can go 100 meters east and 200 meters south.

Answer:

A) 100 meters east and 200 meters south.