Question

The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio. 

Options

• 1 : 3

•  2 : 3

• 3 : 1

• 2 : 3

Answer 1

3 : 1

Explanation: 

Let P(0, y)  be the point of intersection of y-axis with the line segment joining A (−3,−4) and B (1, −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) = ((lambda -3)/(lambda + 1) , (-2lambda -4)/(lambda+1))`

Now equate the x component on both the sides,

`(lambda - 3 ) /(lambda +1) = 0`

On further simplification,

`lambda = 3`

So y-axis divides AB in the ratio `3/1`.