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 2^nd 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 2^nd 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 8^th 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