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Question
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
Options
−a1 : a2
a1 : a2
b1 : b2
−b1 : b2
Solution
Let P( 0 ,y) be the point of intersection of y-axis with the line segment joining` A(a_1 , b_1) " and B " (a_2 , b_2)` which divides the line segment AB 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,
`( 0, y) = ((λa_2 +a_1)/(λ + 1) , ( λb_2 + b_1) /(λ + 1))`
Now equate the x component on both the sides,
`(λa_2 + a_1) /(λ + 1) = 0`
On further simplification,
`λ = - a_1/a_2`
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