Question

Two friends Seema and Aditya work in the same office at Delhi. In the Christmas vacations, both decided to go to their hometowns represented by Town A and Town B respectively in the figure given below. Town A and Town B are connected by trains from the same station C (in the given figure)in Delhi.Based on the given situation, answer the following questions:

(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?

(ii) Seema and Aditya planned to meet at a location D situated at a point D represented by the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by the point D

(iii) Find the area of the triangle formed by joining the points represented by A, B and C.

Answer 1

(i) A(1,7), B(4,2) C(-4,4)

Distance travelled by Seema = √34 units

Distance travelled by Aditya = √68 units

∴ Aditya travels more distance

(ii) Coordinates of D are (1+4/2 , 7+2/2) = (5/2,9/2)

(iii) ar(∆ABC) = 1/2 [ 1(2-4) +4(4-7) -4(7-2)]

= 17 sq. units