Question

To conduct Sport, 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 in 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. 

(i) What is the distance between both the flags ?

(ii) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag ?

(iii) Which mathematical concept is used in the above problem ?

(iv) Which value is depicted in this problem ?

Answer 1

(i) Considering A as origin (0, O), 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)

                   

.'.  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)

                    

.'.  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 blue flag

(ii) Also, Rashmi has to post a blue flag at the mid-point of PQ, therefore by using mid-point formula, we have

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.

(iii) Co-ordinate Geometry.

(iv) Team spirit leads to perfection.