AP EAPCET 23-Aug-2021 Shift 1 Paper

A(−1,−1),B(2,1) and C(3,4),D(1,2)
Then equation of line AB
y−y1=

y2−y1

x2−x1

(x−x1)
⇒y+1=

1+1

2+1

(x+1)
or 3y+3=2x+2 or 2x−3y−1=0 Let the line AB divides the line joining C and D in ratio λ:1, then coordinates of P are P=(

λ+3

λ+1

,

2λ+4

λ+1

)
Since, point P lies on the line AB, putting it in equation of line AB, we obtain
2(

λ+3

λ+1

)−3(

2λ+4

λ+1

)−1=0
⇒2λ+6−6λ−12−λ−1=0
⇒−5λ−7=0
⇒λ=−

7

5

∴λ:1=7:5
Negative sign indicates that line AB intersect it externally.
∴ Desired Ratio =7:5 externally.