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Ex 10.2, 18 - P (a, b) is mid-point of a line segment axes

Ex 10.2, 18 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.2, 18 - Chapter 10 Class 11 Straight Lines - Part 3 Ex 10.2, 18 - Chapter 10 Class 11 Straight Lines - Part 4 Ex 10.2, 18 - Chapter 10 Class 11 Straight Lines - Part 5

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Transcript

Ex 9.2, 17 P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is 𝑥/𝑎 + 𝑦/𝑏 = 2 Plotting x-axis and y-axis Let l be a line intersecting x-axis at A and y-axis at B Let P(a, b) be midpoint of AB Here Let co-ordinates of A be (p, 0) Let co-ordinates of B be (0, q) We know that mid point of a line joining points (x1, y1) & (x2, y2) is ((𝑥_1 − 𝑥_2 )/2, (𝑦_1 − 𝑦_2)/2) Mid point of a line joining points A (p,0) & B(0, q) is P(a,b) Putting values (a, b) = ((𝑝 + 0)/2, (0 + 𝑞)/2) (a, b) = (𝑝/2, 𝑞/2) So, p = 2a, q = 2b So, points A = (p, 0) = (2a, 0) B = (0, q) = (0, 2b) Finding equation of line by two point equation of line (y – y1) = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) (x – x1) For equation of line l passing through (2a, 0) & (0, 2b) Here x1 = 2a, y1 = 0 x2 = 0, y2 = 2b Putting values (y – y1) = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) (x – x1) (y – 0) = (2𝑏 − 0)/(0 − 2𝑎) ( x – 2a) y = 2𝑏/(−2𝑎) (x – 2a) y = (−b)/a (x – 2a) ay = –bx + 2ab ay + bx = 2ab Dividing by ab 𝑎𝑦/𝑎𝑏 + 𝑏𝑥/𝑎𝑏 = 2𝑎𝑏/𝑎𝑏 𝑦/𝑏 + 𝑥/𝑎 = 2 𝑥/𝑎 + 𝑦/𝑏 = 2 Hence, the equation of line is 𝑥/𝑎 + 𝑦/𝑏 = 2 Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.