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 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.

1. What is the distance between the two flags?
2. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post the blue flag?

Answer 1

i. Considering A as origin (0, 0), AB as X-axis and AD as Y-axis.

Niharika runs in the 2^nd line with green flag and distance covered (parallel to AD)

= `1/4 xx 100`

= 25 m

∴ Co-ordinates of green flag are (2, 25) and label it as P i.e., P(2, 25).

Similarly, Preet runs in the eighth line with red flag and distance covered (parallel to AD)

= `1/5 xx 100`

= 20 m

∴ Co-ordinates of red flag are (8, 20) and label it as Q i.e., Q(8, 20)

Now, using distance formula, distance between green flag and flag

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

= `sqrt(6^2 + (-5)^2`

= `sqrt(36 + 25)`

= `sqrt(61)` m

ii. Also, Rashmi has to post a blue flag at the mid-point of PQ, therefore by using mid-point formula, we have `((2 + 8)/2, (25 + 20)/2)` i.e., `(5, 45/2)`

Hence, the blue flag is in the fifth line, at a distance of `45/2` i.e., 22.5 m along the direction parallel to AD.