Question

Point A lies on the line segment XY joining X(6.-6) and Y(-4,-1) in such a way that XA/XY=2/5. If point A also lies on the line 3x+k(y+1)=0, find the value of k

Answer 1

Answer:

The value of k is 2

Step-by-step explanation:

Given:- I) Point A lies on line segment XY having coordinates X(6,-6) and Y(-4,-1)

            II) XA:XY=2:5

                 XA:AY=2:3 [∵AY=XY-XA]

            III) Point A also lies on the line 3x+k(y+1)=0

Formula Used:-Section Formula-> A point (x,y) divides a line segment CD having coordinates C(x₁,y₁) and D(x₂,y₂) in ratio m:n, then coordinates of that point are

x=(m(x₂)+n(x₁))/(m+n)

y=(m(y₂)+n(y₁))/(m+n)

Solution:- Let Point A be (x,y)

  By Section Formula,

 XA:AY=2:3

m=2, n=3

(x₁,y₁)=(6,-6)

(x₂,y₂)=(-4,-1)

x=(m(x₂)+n(x₁))/(m+n)

$x=\frac{2(-4)+3(6)}{2+3}$

$x=\frac{-8+18}{5}$

$x=\frac{10}{5}$

x=2

y=(m(y₂)+n(y₁))/(m+n)

$y=\frac{2(-1)+3(-6)}{2+3}$

$y=\frac{-2-18}{5}$

$y=\frac{-20}{5}$

y=-4

∴Coordinates of Point A is (2,-4)

Point A also lies on line 3x+k(y+1)=0

Putting values of A in above equation

=>    3(2)+k(-4+1)=0

=>     6-3k=0

=>     3k=6

=>      $k=\frac{6}{3}$

=>     k=2

∴  Value of k is 2

Answer 2

Answer:

K=2

Step-by-step explanation:

Refer to attachment...