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 $\frac{1}{4}$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 flags? If Rashmi has to post a blue flag 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 $\frac{1}{4}$ of the distance AD i.e.,
$(\frac{1}{4}\times 100)m=25$ meters from the starting point of the 2nd line.
Therefore, the coordinates of this point G is (2, 25).

Similarly, Preet posted a red flag at $\frac{1}{5}$ of the distance AD i.e.,
$(\frac{1}{5}\times 100)m=20$ meters from the starting point of the 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).
$x=\frac{2+8}{2}$ , $y=\frac{25+20}{2}$
$x=\frac{10}{2}=5$ , $y=\frac{45}{2}=22.5$
Hence, A(x,y)=(5,22.5)

Therefore, Rashmi should post her blue flag at 22.5m on 5th line