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Question 3
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 14th the distance AD on the 2nd line and posts a green flag. Preet runs 15th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?


Solution

It can be observed that Niharika posted the green flag at 14th of the distance AD i.e., (1×1004)m = 25 m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25).
Similarly, Preet posted red flag at 15th of the distance AD i.e., (1×1005)m= 20 m from the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20).
Distance between these flags by using distance formula = GR
=(82)2+(2520)2=36+25=61m
The point at which Rashmi should post her blue flag is the mid-point of the line joining these points.  
Let this point be A (x,y)
x=2+82,y=25+202
x=102,y=452=22.5
Hence, A (x,y) = (5,22.5)
Therefore, Rashmi should post her blue flag at 22.5m on 5th line.

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