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Question:

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags?

Solution:

AD = 100m and AB = 10m
The coordinates of Niharika's flag = (2, 25) and the coordinates of Preet's flag = (8, 20).
A(2, 25) and B(8, 20)
AB = √(20 - 25)² + (8 - 2)² = √(-5)² + 6² = √25 + 36 = √61
Distance between both flags is √61m.
Rashmi has to place her flag at the midpoint of AB.
MIdpoint of AB = ((2 + 8)/2, (25 + 20)/2) = (5, 22.5)
Rashmi must place her flag along the fifth line at 22.5m from A.