Check sibling questions

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Ex 7.4, 1 Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, –2) and B(3, 7). AB is the line segment joining the Points A (2, −2) and B (3, 7) Let line 2x + y − 4 = 0 divide AB in the ratio k : 1 at point P Coordinates of Point P = [(𝑘(3) + 1(2))/(𝑘 + 1),(𝑘(7) + 1(−2))/(𝑘 + 1)] = [(𝟑𝒌 + 𝟐)/(𝒌 + 𝟏),(𝟕𝒌 − 𝟐)/(𝒌 + 𝟏)] Since point P lies on line 2x + y – 4 = 0 Therefore, Putting x = (3𝑘 + 2)/(𝑘 + 1) and y = (7𝑘 − 2)/(𝑘+1) in equation of line 2x + y − 4 = 0 2 ((3𝑘 + 2)/(𝑘+1)) + ((7𝑘 + 2)/(𝑘+1)) − 4 = 0 (2(3𝑘 + 2) + (7𝑘 −2) − 4(𝑘+1))/((𝑘+1)) = 0 6k + 4 + 7k − 2 − 4k − 4 = 0 (k + 1) (6 + 7 − 4)k + 4 − 2 − 4 = 0 9k − 2 = 0 9k = 2 k = 𝟐/𝟗 Thus, ratio in which P divide AB = k : 1 = 2/9 : 1 = 2 : 9

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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.