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  1. Chapter 7 Class 10 Coordinate Geometry
  2. Serial order wise
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Ex 7.4, 1 Determine the ratio in which the line 2x + y โ€“ 4 = 0 divides the line segment joining the points A(2, โ€“2) and B(3, 7). AB is the line segment joining the Points A (2, โˆ’2) and B (3, 7) Let line 2x + y โˆ’ 4 = 0 divide AB in the ratio k : 1 at point P Coordinates of Point P = [(๐‘˜(3) + 1(2))/(๐‘˜ + 1),(๐‘˜(7) + 1(โˆ’2))/(๐‘˜ + 1)] = [(๐Ÿ‘๐’Œ + ๐Ÿ)/(๐’Œ + ๐Ÿ),(๐Ÿ•๐’Œ โˆ’ ๐Ÿ)/(๐’Œ + ๐Ÿ)] . Since point P lies on line 2x + y โ€“ 4 = 0 Therefore, Putting x = (3๐‘˜ + 2)/(๐‘˜ + 1) and y = (7๐‘˜ โˆ’ 2)/(๐‘˜+1) in equation of line 2x + y โˆ’ 4 = 0 2 ((3๐‘˜ + 2)/(๐‘˜+1)) + ((7๐‘˜ + 2)/(๐‘˜+1)) โˆ’ 4 = 0 (2(3๐‘˜ + 2) +(7๐‘˜ โˆ’2) โˆ’ 4(๐‘˜+1))/((๐‘˜+1)) = 0 6k + 4 + 7k โˆ’ 2 โˆ’ 4k โˆ’ 4 = 0 (k + 1) (6 + 7 โˆ’ 4)k + 4 โˆ’ 2 โˆ’ 4 = 0 9k โˆ’ 2 = 0 9k = 2 k = ๐Ÿ/๐Ÿ—. Thus, ratio in which P divide AB = k : 1 = 2/9 : 1 = 2 : 9

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