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  • To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Nihari

3.  To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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

      7.12 figure 

Answers (1)

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Niharika posted the green flag at the distance P, i.e., 

\frac{1}{4}\times100\ m = 25\ m  from the starting point of 2^{nd} line.

Therefore, the coordinates of this point Pare (2,25).

Similarly, Preet posted red flag at \frac{1}{5} of the distance Q i.e., 

\frac{1}{5}\times100\ m = 20\ m  from the starting point of 8^{th} line.

Therefore, the coordinates of this point Q are (8,20).

The distance PQ is given by,

PQ = \sqrt{(8-2)^2+(25-20)^2} = \sqrt{36+25} = \sqrt{61} m

and the point at which Rashmi should post her Blue Flag is the mid-point of the line joining these points. Let this point be R(x,y).

Then, by Section Formula, 

P(x,y)= \left (\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right )

x = \frac{2+8}{2},\ y = \frac{25+20}{2}

x = 5,\ y = 22.5

Therefore, Rashmi should post her Blue Flag at 22.5 m on 5th line.

Posted by

Divya Prakash Singh

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