Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane.

Question 37 (i)

At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1,2), B(4,3) and C(6,6) Slide63.JPG

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Transcript

We know that Diagonals of parallelogram bisect each other So, O is the midβˆ’point of AC & BD Finding midβˆ’point of AC Mid-point of AC = ((π‘₯1 + π‘₯2)/2,(𝑦1 +𝑦2)/2) = ((1 + 6)/2,(2 + 6)/2) = (πŸ•/𝟐,πŸ–/𝟐) Finding midβˆ’point of BD Mid-point of BD = ((π‘₯1 + π‘₯2)/2,(𝑦1 +𝑦2)/2) = ((πŸ’ + 𝒙)/𝟐,(πŸ‘ + π’š)/𝟐) Since O is mid-point of AC and BD ∴ (πŸ•/𝟐,πŸ–/𝟐) =((πŸ’ + 𝒙)/𝟐,(πŸ‘ + π’š)/𝟐) Comparing x and y coordinates Hence , x = 4 , y = 5 Thus, Position of the central midfielder (D) = (x, y) = (3, 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.