Question

Ratio in which the line 3x + 4y = 7 divides the line segment joining the points (1, 2) and (-2,1) is
(a) 3:5
(b) 4:6
(c) 4:9
(d) None of these

Answer 1

Therefore the line $3x+4y=7$ divides the line segment joining the pints $(1,2)$ and $(-2,1)$ in the ratio $4:9$

Step-by-step explanation:

Given;

Let he line $3x+4y=7$ (equation 1) divides the line segment joining the pints 'A' $(1,2)$ and 'B' $(-2,1)$ in the ratio $k:1$ at point 'C'.

From two point 'A' $(1,2)$ and 'B' $(-2,1)$, we get the equation;

$(y-y_{1} )=m(x-x_{1} )$

$(y-2 )=\frac{1-2}{-2-1} (x-1 )$    ( Where $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$)

$3y-6=x-1$

$x-3y=-5$

Above equation multiply with '-3',

$-3x+9y=15$   (equation 2)

Add equation-1 and equation-2,

$13y=22$

$y=\frac{22}{13}$

From equation-1,

$3x+4\times \frac{22}{13} =7$

$x=\frac{1}{13}$

So the intersect point $(\frac{1}{13},\frac{22}{13} )$

Now we know,

$y=\frac{m_{2}y_{1} +m_{1}y_{2}}{m_{1}+m_{2} }$

⇒$\frac{22}{13} =\frac{1\times 2 +k\times1}{k+1}$

⇒$\frac{22}{13} =\frac{ 2 +k}{k+1}$

⇒$26+13k=22k+22$

⇒$9k=4$

⇒$k=\frac{4}{9}$

Thus  the line $3x+4y=7$ divides the line segment joining the pints $(1,2)$ and $(-2,1)$ in the ratio $4:9$

Answer 2

Answer:

the correct answer is (4:9)