Question

If the points $A ( 9,8 , - 10 )$,$B ( 3,2 , - 4 )$and $C ( 5,4 , - 6 )$be collinear, then the point C divides the line $A B$ in the ratio

• A. 2 : 1
• B. 3 : 1
• C. 1 : 2
• D. –1 : 2

Answer 1

Answer: (A)

2 : 1

Answer 2

Let point C divides the line AB in the ratio $1 : \lambda$.

$\therefore 5 = \frac { 9 \lambda + 3 } { \lambda + 1 } \Rightarrow 4 \lambda = 2 \Rightarrow \lambda = \frac { 1 } { 2 }$

Hence required ratio is 2 : 1.