Question

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 $\frac{1}{4}$th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$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?

Answer 1

It can be observed that Niharika posted the green flag at $\frac{1}{4}$th of the distance AD i.e., $\left(\frac{1\times 100}{4}\right)$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 $\frac{1}{5}$th of the distance AD i.e., $\left(\frac{1\times 100}{5}\right)$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
$=\sqrt{(8-2{)}^2+(25-20{)}^2}=\sqrt{36+25}=\sqrt{61}m$
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)
$x=\frac{2+8}{2},y=\frac{25+20}{2}$
$x=\frac{10}{2},y=\frac{45}{2}=22.5$
Hence, A (x,y) = (5,22.5)
Therefore, Rashmi should post her blue flag at 22.5m on 5th line.