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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 

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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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