Find the ratio in which the line 2x+3y-5=0 divides the line segment joining the points8,-9 and 2,1. Also find the co-ordinates of the point of division
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Given the equation of line 2x+3y−5=0
Let A(8,9) and B(2,1) be the points
Let the point of division be of the form K:1 = m:n
Nowx=
m+n
mx
2
+nx
1
=
K+1
K×2+1×8
y=
K+1
my
2
+ny
1
=
K+1
K×1+1×9
⇒(x,y)=(
K+1
2K+8
,
K+1
K+9
)
Substitute (x,y) in the equation
2(
K+1
2K+8
)+3(
K+1
K+9
)−5=0
⇒2(2K+8)+3(K+9)=5(K+1)
⇒4K+16+3K+27=5K+5
⇒2K+38=0∴K=−19
∴ K:1=−19:1=m:n
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