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 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 ?

Explanation

From the above figure, the position of green flag posted by Niharika is `M(2, (1)/(2)xx100)i.e., `
`M(2, 25)` and red flag posted by Preet is `N(8,(1)/(5)xx100)i.e., N(8, 20)`
Now, `MN=sqrt((8-2)^(2)+(20-25)^(2))=sqrt((6)^(2)+(-5)^(2))=sqrt(36+25)=sqrt(61)`
Hence, the distance between flags = `sqrt(61)` m
Let P be the position of the blue flag posted by Rashmi in the halfway of line segment MN.

`therefore" "P` is given by = `((x_(1)+x_(2))/(2), (y_(1)+y_(2))/(2))=((2+8)/(2), (25+20)/(2))=((10)/(2), (45)/(2))=(5, 22.5)`
Hence, the blue flag is on the fifth line at a distance 22.5 m above it.