Question

Kevin hired a cab and followed the path as shown in the figure. if all the distances in the figure are in kilometres. The difference between the total distance and displacement covered by him is ___ km.

Answer 1

Displacement is the shortest distance covered i.e. the distance between the initial and final points.
Displacement of Kevin is, therefore, the shortest distance between mall and hotel.
Distance between two points $(x_1,y_1)and(x_2,y_2)$ is given by $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
Displacement $=\sqrt{(8-2{)}^2+(11-6{)}^2}=\sqrt{6^2+8^2}=10km$

Distance has to be calculated individually between every two points.
Distance between mall and museum = 8 - 3 = 5 km (∵ they are on the same vertical line)
Distance between gallery and museum = 5 - 2 = 3 km (∵ they are on the same horizontal line)
Distance between gallery and park = 15 - 8 = 7 km (∵ they are on the same vertical line)
Distance between hotel and park $=\sqrt{(8-5{)}^2+(11-15{)}^2}=\sqrt{3^2+4^2}=5km$
Total distance covered by Kevin = 5 + 3 + 7 + 5 = 20 km
Distance − Displacement = 20 − 10 = 10 km