In what ratio is the line segment joining the points p(3 -6) and q(5 3) divided by x-axis

Let P (x , 0 )  be the point of intersection of x-axis with the line segment joining A (3,−6) and B (5, 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 ) = ((5λ + 3 ) /(λ + 1 ) , ( 3λ - 6)/(λ + 1))`

Now equate the y component on both the sides,

`(3λ - 6 ) / (λ + 1 )=0`

On further simplification,

`λ = 2/1`

So x-axis divides AB in the ratio 2:1.

CBSE 10 - Maths

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Asked by Trisha Gupta | 03 Nov, 2021, 12:44: AM

ANSWERED BY EXPERT

CBSE 10 - Maths

solve

Asked by Trisha Gupta | 03 Nov, 2021, 12:44: AM

ANSWERED BY EXPERT