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Ex 7.2, 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 1/4th 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? Here let us draw a simpler figure of what is given Here , given that there are 100 flowers between A & D at 1m distance each Niharika runs 1/4th of the distance AD on 2nd line So, Niharika x−ordinate = 2 Niharika y – ordinate = 1/4 × 100 = 25 So, Niharika (2, 25) Similarly, Preet runs 1/5th of the distance AD on 2nd line So, Preet x−ordinate = 8 Preet y – ordinate = 1/5 × 100 = 20 So, Preet (8, 20) We have to find distance between Niharika and Preet’s flag Using distance formula NP = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) x1 = 2, y1 = 25 x2 = 8, y2 = 20 Putting values in formula NP = √(( 8 −2)2+(20 −25)2) = √((6)2+(−5)2) = √((6)2+(5)2) = √(36+25) = √61 Hence, The distance between both flags = √𝟔𝟏 metres Also, it is given that Rashmi had to post a blue flag exactly halfway between the line segment joining the two flags So, Here, x = (𝑥1 + 𝑥2)/2 y = (𝑦1 + 𝑦2)/2 Where x1 = 2, y1 = 25 x2 = 8, y2 = 20 Substituting the value in the formula x = 5, y = 22.5 Therefore, Rashmi (x, y) = (5, 22.5) Therefore Rashmi would post her flag in the 5th line at 22.5 metre x = (𝑥1 + 𝑥2)/2 x = (2 + 8)/2 x = 10/2 x = 5 y = (𝑦1 + 𝑦2)/2 y = (25 + 20)/2 y = 45/2 y = 22.5

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.