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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 𝑥/𝑎 + (𝑦 )/𝑏 = 1 Coordinate of point which divide line segment joining two points (x1, y1) & (x2, y2) in the ratio of m1 : m2 are = ((𝑚_2 𝑥_2 + 𝑚_1 𝑥_1)/(𝑚_1 + 𝑚_2 ),(𝑚_2 𝑦_(2 ) + 𝑚_1 𝑦_1)/(𝑚_1 + 𝑚_2 )) Point R(h, k) divide AB joining two points (a, 0) & (0, b) in ratio of 1 : 2 (h, k) = ((1 × 0 + 2 × 𝑎)/(1 + 2), (1 × 𝑏 + 2 × 0)/(1 + 2)) (h, k) = ((0 + 2𝑎)/3, 𝑏/3) (h, k) = (2𝑎/3, 𝑏/3) 𝟐𝒂/𝟑 = h 2a = 3h a = 3ℎ/2 𝒃/𝟑 = k b = 3k Putting value of a & b in (1) 𝑥/𝑎 + (𝑦 )/𝑏 = 1 𝑥/(3ℎ/2) + (𝑦 )/3𝑘 = 1 2𝑥/3ℎ + (𝑦 )/3𝑘 = 1 1/3 (2𝑥/ℎ+ (𝑦 )/𝑘) = 1 (2𝑥(𝑘) + 𝑦(ℎ))/ℎ𝑘 = 1 × 3 (2𝑘𝑥 + ℎ𝑦)/(ℎ𝑘 ) = 3 2kx + hy = 3hk Which is the required equation

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

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.