Question

ratio in which the line 3x+4y =7 divides the line segment joining the points (1,2) and (_2,1)is
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Answer 1

Ratio in which the line segment divides the point is $4:9$

Step-by-step explanation:

Lets assign $(x_1,y_1)$ to $(1,2)$ and $(x_2,y_2)$ with $(-2,1)$.

Using the point slope formula we will find the equation of the another line comprises those points.

So,

⇒$y-y_1=m(x-x_1)$ choosing  $(-2,1)$ as the reference points.

⇒$(y-2)=\frac{1-2}{-2-1}(x-1)$

⇒$x-3y=-5$  equation $(1)$

And $3x+4y=7$ as equation $(2)$

• Solving both the equations.

$x-3y=-5$ multiplying with $3$

$3x-9y=-15$  equation $(1)$

$3x+4y=7$ equation $(2)$

• Subtracting both the equations and solving it we have the coordinates between  $(1,2)$,$(-2,1)$ .

And that are $(\frac{1}{13},\frac{22}{13} )$

• Now we will say that  $(\frac{1}{13},\frac{22}{13} )$ divides the line segment in $k:1$ ratios.

And we will use section formula along with any of the values of either x or y.

To find the ratios:

$x=\frac{m_2x_1\ + m_1x_2}{m_1+m_2}$

Then,

$\frac{1}{13} =\frac{(1\times 1)+(k\times -2)}{k+1}$

$k+1=13-26k$

$27k=12$

$k=\frac{4}{9}$

So the ratios which we have assumed $k:1=4:9$

The line segment will be divided by $4:9$ by the points comprising that lines.