find the ratio in which the line 2x+3y-5=0 divides the line segment joining the points (8;-9) and (2;1) .also find the coordinates of the point of division
Answers
Answered by
2
let line divides 2x+3y-5=0 to the segment joining (8,-9) and (2,1) in k:1
let point of intersect be (a,b)
by intersection formula
(a,b)=(2k+8/k+1 , k-9/k+1)
a=2k+8/k+1 and b=k-9/k+1
these point will also lie on line 2x+3y-5=0.hence point will satisfy this equation
2×2k+8/k+1 + 3×k-9/k+1 -5 =0
4k+16+3k-27-5k-5=0
2k-16=0
k=8
ratio will be 8:1
coordinate will be x=2k+8/k+1=24/9 and y=k-9/k+1=-1/9
let point of intersect be (a,b)
by intersection formula
(a,b)=(2k+8/k+1 , k-9/k+1)
a=2k+8/k+1 and b=k-9/k+1
these point will also lie on line 2x+3y-5=0.hence point will satisfy this equation
2×2k+8/k+1 + 3×k-9/k+1 -5 =0
4k+16+3k-27-5k-5=0
2k-16=0
k=8
ratio will be 8:1
coordinate will be x=2k+8/k+1=24/9 and y=k-9/k+1=-1/9
Similar questions