Question

Carpooling is the sharing of car journeys so that more than one person travels in a car, and prevents the need for others to have to drive to a location themselves. By having more people using one vehicle, carpooling reduces each person’s travel costs such as: fuel costs, tolls, and the stress of driving. Carpooling is also a more environmentally friendly and sustainable way to travel as sharing journeys reduces air pollution, carbon emissions, traffic congestion on the roads, and the need for parking spaces. Three friends Amar, Bhavin and Chetanya live in societies represented by the points A(4, 5), B(6, 2) and C(2, 6) respectively. They all work in offices located in a same building represented by the point O(0, 0). Since they all go to same building every day, they decided to do carpooling to save money on petrol.

Based on the above information, answer the following questions.

1. What is the distance between B and C?   (1)
2. If Bhavin and Chetanya planned to meet at a club situated at the mid-point of the line joining the points B and C, find the coordinates of this point.   (1)
3. 1. Which society is farthest from the office? Also find its distance from the office.   (2)
      OR
   2. Out of B and C which society is nearer to A? Also find their distances.

Answer 1

1. Distance between B and C = `4sqrt(2)` units.
2. Mid-point of the line joining the points B and C = (4, 4).
3. 1. As, OA = `sqrt(41)` units, OB = `sqrt(40)` units, OC = `sqrt(40)` units.
      So, society A is the farthest from the office.
      OR
   2. As, AB = `sqrt(13)` units, AC = `sqrt(5)` units.
      So, Society C is nearer to society A.