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 \( \dfrac{1}{4}\) th the distance AD on the 2nd line and posts a green flag. Preet runs \( \dfrac{1}{5}^{th}\) 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?

Asked by Abhisek | 1 year ago |  68

1 Answer

Solution :-

From the given instruction, we observed that Niharika posted the green flag at 

\( \dfrac{1}{4}^{th}\) of the distance AD i.e., (\( \dfrac{1}{4}\) ×100) m = 25 m from the starting point of \( 2^{nd}\) line. 

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

Similarly, Preet posted red flag at \( \dfrac{1}{5}\) of the distance AD i.e., (\( \dfrac{1}{5}\) ×100) m 

= 20m from the starting point of \( 8^{th}\) line. 

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

Distance between these flags can be calculated by using distance formula,

NCERT Solutions for Class 10 Chapter 7-17

The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. 

Let say this point be P(x, y).

x = \( \dfrac{2+8}{2}\)\( \dfrac{10}{2}\) = 5 and y = \( \dfrac{(20 + 25)}{2}\) =\( \dfrac{45}{2}\)

Hence, P( xy) = (5,\( \dfrac{45}{2}\))

Therefore, Rashmi should post her blue flag at \( \dfrac{45}{2}\)= 22.5 m on \( 5^{th}\) line.

Answered by Pragya Singh | 1 year ago

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