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Section Formula- Finding coordinates of a point in a quadrilateral

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Ex 7.2 , 6 If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. Let the points be A(1, 2), B(4, y), C(x, 6), D(3, 5) We know that diagonals of parallelogram bisect each other So, O is the mid−pint of AC & BD Finding mid−point of AC We have to find co−ordinates of O x−coordinate of O = (𝑥1 + 𝑥2)/2 y−coordinate of O = (𝑦1 + 𝑦2)/2 Where x1 = 1, y1 = 2 x2 = x, y2 = 6 Putting values for x−coordinate x−coordinate of O = (1 + 𝑥)/2 Putting values for y−coordinate y−coordinate of O = (2 + 6)/2 = 8/2 = 4 Hence, coordinates of O = ((1 + 𝑥)/2 ", 4" ) Finding mid−point of BD, We find coordinates of O x−coordinate of O = (𝑥1 + 𝑥2)/2 y−coordinate of O = (𝑦1 + 𝑦2)/2 x1 = 4, y1 = y x2 = 3, y2 = 5 Putting values for x−coordinate x−coordinate of O = (4 + 3)/2 x−coordinate of O = 7/2 Putting values for y−coordinate y−coordinate of O = (𝑦 + 5)/2 Hence, coordinates of O = (7/2 " , " (𝑦 + 5)/2) Comparing x & y coordinates Hence , x = 6 , y = 3 (1 + 𝑥)/2 = 7/2 (1 + x) = 7 x = 7 – 1 x = 6 4 = (𝑦 + 5)/2 4 × 2 = y + 5 8 – 5 = y 3 = y y = 3

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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.