Check sibling questions

Ex 10.2, 19 - Point R (h, k) divides a line between axes

Ex 10.2, 19 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.2, 19 - Chapter 10 Class 11 Straight Lines - Part 3

This video is only available for Teachoo black users

 

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


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 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

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.