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Section Formula- Finding coordinates of a point in a quadrilateral

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Example 10 If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p. Let the points be A(6, 1) , B(8, 2) C(9, 4) , D(p, 3) We know that diagonals of parallelogram bisect each other So, O is the mid−pint of AC & BD ∴ We find x co−ordinate of O from both AC & BD Finding mid−point of AC We have to find x co−ordinate of O x−coordinate of O = (𝑥1 + 𝑥2)/2 Where x1 = 6, x2 = 9, Putting values for x−coordinate x−coordinate of O = (6 + 9)/2 = 𝟏𝟓/𝟐 Finding mid−point of BD We have to find x co−ordinate of O x−coordinate of O = (𝑥1 + 𝑥2)/2 Where x1 = 8 , x2 = p , Putting values for x−coordinate x−coordinate of O = (8 + 𝑝)/2 Comparing (1) & (2) 15/2 = (8 + 𝑝)/2 15 = 8 + p 15 = 8 + p 15 – 8 = p 7 = p p = 7 Hence, p = 7

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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.