IMAT 2017 Q53 [Displacement]

A car starts at point X. It travels 3.0 km due east, then 4.0 km due south, then
6.0 km due west and finally 8.0 km due north.

How far away is the car from point X when it has reached the end of this journey?

[Assume that all distances moved are on a flat horizontal surface, and that point X is on the equator. You may ignore any curvature of the Earth.]

A. 5.0 km
B. 21.0 km
C. 10.0 km
D. 7.0 km
E. 2.0 km

The best way to solve this is to draw the movement of the car:

Looking at the movement, we can see that the distance (d) from the start is actually the diagonal of a rectangle with the sides: 4km and 3km.

In order to calculate the distance, we will use the Pythagoras’ theorem: d^2 = (4km)^2 + (3km)^2 = 16 km^2 + 9 km^2 = 25 km^2 \to d = \sqrt{25 km^2} = 5 km

So, the correct answer is (A) 5km.