Question

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 `1/4` th the distance AD on the 2^nd 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?

Answer 1

It can be observed that Niharika posted the green flag at `1/4`th of the distance AD i.e., `(1×100/4)` m = 25m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25). Similarly, Preet posted red flag at` 1/5` of the distance AD i.e., `(1×100/5)` m = 20m 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

GR = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

= `sqrt((8-2)^2+(25-20)^2)`

= `sqrt(36+25)`

= `sqrt61` 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 = `(2+8)/2`

y = `(25+20)/2`

x = `10/2`

x = 5

y = `45/2`

y = 22.5

Hence, A(x, y) = (5, 22.5)

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