# 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?

The green flag is $$\frac{1}{4} th$$ of total distance =
$$\frac{1}{4} × 100 = 25$$ m in second line

$$\therefore$$ the coordinate of green flag
= (2 , 25 )
Similarly coordinate of red flag
= (8 , 20)

Distance between red and green flag
= $$\sqrt{(8-2)^2 + (20-25)^2}$$
$$= \sqrt{6^2+(-5)^2}$$
$$= \sqrt{36+25}$$
$$= \sqrt{61} m$$

Now blue flag is posted at the mid point of two flag
Then let, the coordinate of blue flag = (x , y )

$$\therefore( x , y ) =( \frac{(8+2)}{2} , \frac{20+25}{2} )$$
$$=( 5 , \frac{45}{2} )= ( 5, 22.5 )$$

$$\therefore$$ the blue flag is posted in fifth line at a distance of 22.5 m