Question

 The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is

Options

• 2: 1

• 1 : 2

• −2 : 1

•  1 : −2

Answer 1

Let P(x , 0 )  be the point of intersection of x-axis with the line segment joining A (3, 6) and B (12, −3) 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,

`(x , 0) = ((12lambda + 3 ) / ( lambda + 1) , (-3lambda + 6 ) / ( lambda + 1 )) `

Now equate the y component on both the sides,

`(-3lambda + 6 )/(lambda + 1) = 0`

On further simplification,

`lambda = 2/1`

So x-axis divides AB in the ratio `2/1`