Question

7. Find the ratio in which the line2x+3y=10 divides the line segment joining
the points (1, 2) and (2, 3).

Answer 1

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