Question

If the line joining the points (6, 6) and (1, – 3) is divided by the line x + λy = 2, internally in the ration 2 : 3 , then the value of $\lambda$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Coordinates of the point P, dividing the join of A(6, 6) and B(1, – 3) in the ratio 2 : 3 are
$\alpha =\frac{2\left(1\right)+3\left(6\right)}{2+3}$

$=\frac{20}{5}=4and\beta =\frac{2(-3)+3\left(6\right)}{2+3}=\frac{-6+18}{5}=\frac{12}{5}\therefore \left(\alpha \beta \right)\equiv (4,\frac{12}{5})$
$SincethepointPliesonthelinex+\lambda y=2\therefore 4+\lambda \left(\frac{12}{5}\right)=2or\lambda =-\frac{5}{6}$