The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is

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Let C( x , 0) be the point of intersection of x-axis with the line segment joining p(x1 , y1) and Q(x2,y2) which divides the line segment PQ in the ratio λ : 1 . Now according to the section formula if point a point P divides a line segment joining `A(x_1 ,y_1) " and B " (x_2 , y_2) `in the ratio m:n internally than, `P(x ,y) = ((nx_1 + mx_2)/(m + n) , (ny_1 + my_2)/(m + n))` Now we will use section formula as, `(x , 0) = ((λx_2 + x_1)/(λ+1) , (λy_2 + y_1)/(λ + 1))` Now equate the y component on both the sides, (λy_2 + y_1)/(λ + 1) = 0 On further simplification, λ = ( y_1) /(y_2)

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