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Last updated at Feb. 3, 2020 by Teachoo
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Ex 10.2, 18 P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is ๐ฅ/๐ + ๐ฆ/๐ = 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 ((๐ฅ_1 โ ๐ฅ_2 )/2, (๐ฆ_1 โ ๐ฆ_2)/2) Mid point of a line joining points A (p,0) & B(0, q) is P(a,b) Putting values (a, b) = ((๐ + 0)/2, (0 + ๐)/2) (a, b) = (๐/2, ๐/2) 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 โ y1) = (๐ฆ_2 โ ๐ฆ_1)/(๐ฅ_2 โ ๐ฅ_1 ) (x โ x1) For equation of line l passing through (2a, 0) & (0, 2b) Here x1 = 2a, y1 = 0 x2 = 0, y2 = 2b Putting values (y โ y1) = (๐ฆ_2 โ ๐ฆ_1)/(๐ฅ_2 โ ๐ฅ_1 ) (x โ x1) (y โ 0) = (2๐ โ 0)/(0 โ 2๐) ( x โ 2a) y = 2๐/(โ2๐) (x โ 2a) y = (โb)/a (x โ 2a) ay = โbx + 2ab ay + bx = 2ab Dividing by ab ๐๐ฆ/๐๐ + ๐๐ฅ/๐๐ = 2๐๐/๐๐ ๐ฆ/๐ + ๐ฅ/๐ = 2 ๐ฅ/๐ + ๐ฆ/๐ = 2 Hence, the equation of line is ๐ฅ/๐ + ๐ฆ/๐ = 2 Hence proved
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