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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 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 `1/5` th 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 `1/4`th of the distance AD i.e., `(1×100/4)` m = 25m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25). Similarly, Preet posted red flag at` 1/5` of the distance AD i.e., `(1×100/5)` m = 20m 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
GR = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((8-2)^2+(25-20)^2)`
= `sqrt(36+25)`
= `sqrt61` m
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+8)/2`
y = `(25+20)/2`
x = `10/2`
x = 5
y = `45/2`
y = 22.5
Hence, A(x, y) = (5, 22.5)
Therefore, Rashmi should post her blue flag at 22.5 m on 5th line.
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