Ex 10.2

Ex 10.2, 1
Important

Ex 10.2, 2

Ex 10.2, 3

Ex 10.2, 4 Important

Ex 10.2, 5

Ex 10.2, 6 Important

Ex 10.2, 7

Ex 10.2, 8 Important

Ex 10.2, 9 Important

Ex 10.2, 10

Ex 10.2, 11 Important

Ex 10.2, 12

Ex 10.2, 13

Ex 10.2, 14 Important

Ex 10.2, 15 Important

Ex 10.2, 16

Ex 10.2, 17 Important

Ex 10.2, 18 Important You are here

Ex 10.2, 19 Important

Ex 10.2, 20

Last updated at Feb. 3, 2020 by Teachoo

Ex 10.2, 18 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