Intercept form
Last updated at April 16, 2024 by Teachoo
Ex 9.2, 18 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 π₯/π + (π¦ )/π = 1 Coordinate of point which divide line segment joining two points (x1, y1) & (x2, y2) in the ratio of m1 : m2 are = ((π_2 π₯_2 + π_1 π₯_1)/(π_1 + π_2 ),(π_2 π¦_(2 ) + π_1 π¦_1)/(π_1 + π_2 )) Point R(h, k) divide AB joining two points (a, 0) & (0, b) in ratio of 1 : 2 (h, k) = ((1 Γ 0 + 2 Γ π)/(1 + 2), (1 Γ π + 2 Γ 0)/(1 + 2)) (h, k) = ((0 + 2π)/3, π/3) (h, k) = (2π/3, π/3) ππ/π = h 2a = 3h a = 3β/2 π/π = k b = 3k Putting value of a & b in (1) π₯/π + (π¦ )/π = 1 π₯/(3β/2) + (π¦ )/3π = 1 2π₯/3β + (π¦ )/3π = 1 1/3 (2π₯/β+ (π¦ )/π) = 1 (2π₯(π) + π¦(β))/βπ = 1 Γ 3 (2ππ₯ + βπ¦)/(βπ ) = 3 2kx + hy = 3hk Which is the required equation