Question

point A lies on the line segment xy joining x (6, - 6) Y (- 4 ,-1) in such a way that X A upon x y is equals to 2 upon 3.if Also lies on the line 3 X + K( Y + 1)=0 .

find the value of k​.........

Answer 1

A lies on the line segment xy joining X(6,-6) , Y(-4,-1) in such a way that XA/XY = 2/3

or, XA/(XA + AY) = 2/3

or, 3XA = 2XA + 2AY

or, XA = 2AY

or, XA/AY = 2/1

it means, A divides the line XY in the ratio of 2 : 1.

use section formula to find coordinate of A.

$A=\left(\frac{2\times-4+1\times6}{2+1},\frac{2\times-1+1\times-6}{2+1}\right)$

= (-2/3 , -8/3)

now, A lies on the line 3x + k(y + 1) = 0

put (-2/3, -8/3) in 3x + k(y + 1) = 0

or, 3 × (-2/3) + k(-8/3 + 1) = 0

or, -6 - 5k = 0

or, k = -6/5