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  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise

Transcript

Ex 10.2, 19 Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find equation of the line. Let the AB be a line between axis & point R(h, k) divides AB in the ratio 1: 2 Let AB make x-intercept a & y-intercept b Point A = (a, 0) & B = (0, b) So, equation of line AB by intercept form is ๐‘ฅ/๐‘Ž + (๐‘ฆ )/๐‘ = 1 Coordinate of point which divide line segment joining two points (x1, y1) & (x2, y2) in the ratio of m1 : m2 are = ((๐‘š_2 ๐‘ฅ_2 + ๐‘š_1 ๐‘ฅ_1)/(๐‘š_1 + ๐‘š_2 ),(๐‘š_2 ๐‘ฆ_(2 ) + ๐‘š_1 ๐‘ฆ_1)/(๐‘š_1 + ๐‘š_2 )) Point R(h, k) divide AB joining two points (a, 0) & (0, b) in ratio of 1 : 2 (h, k) = ((1 ร— 0 + 2 ร— ๐‘Ž)/(1 + 2), (1 ร— ๐‘ + 2 ร— 0)/(1 + 2)) (h, k) = ((0 + 2๐‘Ž)/3, ๐‘/3) (h, k) = (2๐‘Ž/3, ๐‘/3) ๐Ÿ๐’‚/๐Ÿ‘ = h 2a = 3h a = 3โ„Ž/2 ๐’ƒ/๐Ÿ‘ = k b = 3k Putting value of a & b in (1) ๐‘ฅ/๐‘Ž + (๐‘ฆ )/๐‘ = 1 ๐‘ฅ/(3โ„Ž/2) + (๐‘ฆ )/3๐‘˜ = 1 2๐‘ฅ/3โ„Ž + (๐‘ฆ )/3๐‘˜ = 1 1/3 (2๐‘ฅ/โ„Ž+ (๐‘ฆ )/๐‘˜) = 1 (2๐‘ฅ(๐‘˜) + ๐‘ฆ(โ„Ž))/โ„Ž๐‘˜ = 1 ร— 3 (2๐‘˜๐‘ฅ + โ„Ž๐‘ฆ)/(โ„Ž๐‘˜ ) = 3 2kx + hy = 3hk Which is the required equation

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.