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Ex 10.2, 18 - P (a, b) is mid-point of a line segment axes - Intercept form

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Ex10.2, 18 P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is ๐‘ฅ/๐‘Ž + ๐‘ฆ/๐‘ = 2 Plotting x-axis and y-axis Let l be a line intersecting x-axis at A and y-axis at B Let P(a, b) be midpoint of AB Here Let co-ordinates of A be (p, 0) Let co-ordinates of B be (0, q) We know that mid point of a line joining points (x1, y1) & (x2, y2) is ((๐‘ฅ1 + ๐‘ฅ2 )/2, (๐‘ฆ1 + ๐‘ฆ2)/2) Mid point of a line joining points A (p,0) & B(0, q) is P(a,b) Putting values (a, b) = ((๐‘ + 0)/2, (0 + ๐‘ž)/2) (a, b) = (๐‘/2, ๐‘ž/2) So, p = 2a, q = 2b So, points A = (p, 0) = (2a, 0) B = (0, q) = (0, 2b) Finding equation of line by two point equation of line (y โ€“ y1) = (๐‘ฆ_2 โˆ’ ใ€– ๐‘ฆใ€—_1)/(๐‘ฅ_2 โˆ’ ใ€– ๐‘ฅใ€—_1 ) (x โ€“ x1) For equation of line l passing through (2a, 0) & (0, 2b) Here x1 = 2a, y1 = 0 x2 = 0, y2 = 2b Putting values (y โ€“ y1) = (๐‘ฆ_2 โˆ’ ใ€– ๐‘ฆใ€—_1)/(๐‘ฅ_2 โˆ’ ใ€– ๐‘ฅใ€—_1 ) (x โ€“ x1) (y โ€“ 0) = (2๐‘ โˆ’ 0)/(0 โˆ’ 2๐‘Ž) ( x โ€“ 2a) y = 2๐‘/( โˆ’ 2๐‘Ž) (x โ€“ 2a) y = ( โˆ’ b)/a (x โ€“ 2a) ay = โ€“bx + 2ab ay + bx = 2ab Dividing by ab ๐‘Ž๐‘ฆ/๐‘Ž๐‘ + ๐‘๐‘ฅ/๐‘Ž๐‘ = 2๐‘Ž๐‘/2๐‘Ž๐‘ ๐‘ฆ/๐‘ + ๐‘ฅ/๐‘Ž = 2 ๐‘ฅ/๐‘Ž + ๐‘ฆ/๐‘ = 2 Hence ,the equation of line is ๐‘ฅ/๐‘Ž + ๐‘ฆ/๐‘ = 2 Hence proved

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