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