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Solution


Q.

Shown below is a map of Giri’s neighbourhood. Giri did a survey of his neighbourhood and collected the following information

  • The hotel, mall and the main gate of the garden lie in a straight line.
  • The distance between the hotel and the mall is half of the distance between the mall and the main gate of the garden.
  • The bus stand is exactly midway between the main gate of the garden and the fire station.
  • The mall, bus stand and the water tank lie in a straight line.

Based on the above information, answer the following questions:

 

(i) What is the x-coordinate of the mall’s location
1 0  
2 1  
3 2  
4 4  

Ans.

(1)

Since the distance between the hotel (H) and the mall (M) is half of the distance between the mall and the main gate (Mg):

MgMMH=21⇒MgM:MH=2:1

 

Using section formula, coordinates of mall M(x,y) are given by:

x=2×(-2)+1×42+1,y=2×5+1×172+1⇒x=0,y=273=9

Thus, x-coordinate of mall is 0.