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Last updated at Feb. 3, 2020 by Teachoo

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 ๐ฅ/๐ + (๐ฆ )/๐ = 1 Coordinate of point which divide line segment joining two points (x1, y1) & (x2, y2) in the ratio of m1 : m2 are = ((๐_2 ๐ฅ_2 + ๐_1 ๐ฅ_1)/(๐_1 + ๐_2 ),(๐_2 ๐ฆ_(2 ) + ๐_1 ๐ฆ_1)/(๐_1 + ๐_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)/(1 + 2), (1 ร ๐ + 2 ร 0)/(1 + 2)) (h, k) = ((0 + 2๐)/3, ๐/3) (h, k) = (2๐/3, ๐/3) ๐๐/๐ = h 2a = 3h a = 3โ/2 ๐/๐ = k b = 3k Putting value of a & b in (1) ๐ฅ/๐ + (๐ฆ )/๐ = 1 ๐ฅ/(3โ/2) + (๐ฆ )/3๐ = 1 2๐ฅ/3โ + (๐ฆ )/3๐ = 1 1/3 (2๐ฅ/โ+ (๐ฆ )/๐) = 1 (2๐ฅ(๐) + ๐ฆ(โ))/โ๐ = 1 ร 3 (2๐๐ฅ + โ๐ฆ)/(โ๐ ) = 3 2kx + hy = 3hk Which is the required equation

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About the Author

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.