Question

# Question 3 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 14th the distance AD on the 2nd line and posts a green flag. Preet runs 15th 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?

Solution

## It can be observed that Niharika posted the green flag at 14th of the distance AD i.e., (1×1004)m = 25 m from the starting point of 2nd line. Therefore, the coordinates of this point G is (2, 25). Similarly, Preet posted red flag at 15th of the distance AD i.e., (1×1005)m= 20 m from the starting point of 8th line. Therefore, the coordinates of this point R are (8, 20). Distance between these flags by using distance formula = GR =√(8−2)2+(25−20)2=√36+25=√61m The point at which Rashmi should post her blue flag is the mid-point of the line joining these points.   Let this point be A (x,y) x=2+82,y=25+202 x=102,y=452=22.5 Hence, A (x,y) = (5,22.5) Therefore, Rashmi should post her blue flag at 22.5m on 5th line.

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