Question

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

Ans - _

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 the mall and the 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 $=\sqrt{(8-2{)}^2+(11-3{)}^2}=\sqrt{6^2+8^2}=10km$
Distance has to be calculated between every two points.
Distance between the mall and the museum = 8 - 3 = 5 km(They are on the same vertical line)
Distance between the gallery and trhe museum = 5 - 2 = 3 km(They are on the same horizontal line.)
Distance between the gallery and the park = 15 - 8 = 7 km(They are on the same vertical line)
Distance between the hotel and the 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.