**Ex 7.2, 6**

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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) From (1) & (2) ((1 + 𝑥)/2 , 4) = (7/2 , (𝑦 + 5)/2) Comparing x & y coordinates Hence , x = 6 , y = 3

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