UPSC NDA Math Model Paper 8

Given: Point (1, 2) divides the line passing through (h, 0) and (0, k) in the ratio 2:3
Here,m:n=2:3,(x,y)=(1,2), (x1,y1)=(0,k),(x2,y2)=(h,0)
∴x=

mx2+nx1

m+n

⇒1=

2(h)+3(0)

2+3

⇒1=

2h

5

⇒2h=5
⇒h=

5

2

y=

my2+ny1

m+n

⇒2=

2(0)+3(k)

2+3

⇒3k=2(5)=10
⇒k=

10

3

∴ points are (

5

2

,0) and (0,

10

3

)
Now, equation of line passing through (

5

2

,0) and (0,

10

3

)

x

5 2

+

y

10 3

=1
⇒

2x

5

+

3y

10

=1
⇒4x+3y=10 (multiply whole equation by 10)
Hence, option (4) is correct.