Question

Find the ratio in which the line x+3y-14=0 divides the line segment joining the points A(-2,4) B(3,7).

Answer 1

Answer:

The line x+3y-14=0 divides the line segment joining (-2,4) and (3,7) in the ratio 2:5

Step-by-step explanation:

$\textsf{Concept:}$

$\textsf{The co ordinates of the point which divides the line segment joining}$$\textsf{ (x_1,y_1) and (x_2,y_2) internally in the ratio m:n is}$

$\displaystyle\mathsf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\textsf{Let P be the point on the line x+3y-14=0 which divides}$$\textsf{ line joining A(-2,4) and B(3,7) internally in the ratio m:n}$

$\textsf{Then, the coordinates P is}$

$\displaystyle\mathsf(\frac{m(3)+n(-2)}{m+n},\frac{m(7)+n(4)}{m+n})$

$\displaystyle\mathsf{(\frac{3m-2n}{m+n},\frac{7m+4n}{m+n})}$

$\textsf{since P lies on the line x+3y-14=0, we have}$

$\displaystyle\mathsf{(\frac{3m-2n}{m+n})+3(\frac{7m+4n}{m+n})-14=0}$

$\implies\mathsf{(3m-2n)+3(7m+4n)-14(m+n)=0}$

$\implies\mathsf{3m-2n+21m+12n-14m-14n=0}$

$\implies\mathsf{10m-4n=0}$

$\implies\mathsf{5m=2n}$

$\implies\mathsf{\frac{m}{n}=\frac{2}{5}}$

$\implies\boxed{\mathsf{m:n=2:5}}$

Answer 2

Answer:

The line x+3y-14=0 divides the line segment joining (-2,4) and (3,7) in the ratio 2:5

The line x+3y-14=0 divides the line segment joining (-2,4) and (3,7) in the ratio 2:5Step-by-step explanation:

The line x+3y-14=0 divides the line segment joining (-2,4) and (3,7) in the ratio 2:5Step-by-step explanation:\textsf{Concept:}Concept:

The line x+3y-14=0 divides the line segment joining (-2,4) and (3,7) in the ratio 2:5Step-by-step explanation:\textsf{Concept:}Concept:\sorry dont know