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 1/4 th 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 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?
From the given instruction, we observed that Niharika posted the green flag at 1/4th of the distance AD i.e., (1/4 ×100) m = 25 m from the starting point of 2nd line.
Therefore, the coordinates of this point are (2, 25).
Similarly, Preet posted red flag at 1/5 of the distance AD i.e., (1/5 ×100) m = 20m from the starting point of 8th line.
Therefore, the coordinates of this point are (8, 20).
Distance between two flags
= \(\sqrt{(8-2)^2 + (20-25)^2}\)
= \(\sqrt{36+25}\)
= \(\sqrt{61}\)
Let say this point be P(x, y).
x = (2 + 8)/2 = 10/2 = 5 and
y = (20 + 25)/2 = 45/2
Hence, P( x, y) = (5, 45/2)
Therefore, Rashmi should post her blue flag at 45/2 = 22.5m on 5th line.