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

##### 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,

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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