question_answer

In what ratio does the line \[4x+3y-13=0\] divide the line segment joining the points (2, 1) and (1, 4)?

A)  \[3:2\] internally            

B)  \[2:3\]internally

C)  \[2:3\] externally        

D)  \[3:2\]externally

Correct Answer: B

Solution :

(b): Let line joining (2, 1) and (1, 4) be divided in the ratio \[K:1\]at intersection point C. \[\therefore \] Coordinates of' ?C? will be \[\left( \frac{K+2}{K+1},\frac{4K+1}{K+1} \right)\] ?C? also lies on line \[4x+3y-13=0\] \[\Rightarrow \]\[4\left( \frac{K+2}{K+1} \right)+3\left( \frac{4K+1}{K+1} \right)-13=0\] \[\Rightarrow \]\[4K+8+12K+3-13=0\] \[\Rightarrow \]\[3K=13-11\] \[\Rightarrow \]\[3K=2\] \[\Rightarrow \]\[K:1=2:3\]