Question

Equation of the line whose portion intercepted between the axes is divided by the

point(3,4) in the ratio 1:2​

Answer 1

Step-by-step explanation:

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Answer 2

The equation of the line whose portion intercepted between the axes is divided by the point (3,4) in the ratio 1 : 2 is

2x + 3y = 18

Step-by-step explanation:

Let the coordinates of the points where the line cuts the x-axis and y-axis be (a,0) and (0,b)

Given that point (3, 4) divides the line joining (0, b) and (a, 0) in the ratio 1:2

We know that if a point P(x,y) divides line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m:n

Then

$x=\frac{mx_2+nx_1}{m+n}$

And

$y=\frac{my_2+ny_1}{m+n}$

Thus,

$3=\frac{1\times a+2\times 0}{1+2}$

$\implies a=9$

Similarly,

$4=\frac{1\times 0+2\times b}{1+2}$

$\implies 12=2b$

$\implies b=6$

The equation of line whose x and y intercepts are a and b is given by

$\frac{x}{a}+\frac{y}{b}=1$

Therefore,  the equation of line

$\frac{x}{9}+\frac{y}{6}=1$

$\frac{x}{3}+\frac{y}{2}=3$

$\implies 2x+3y=18$

This is the equation of the line.

Hope this answer is helpful.

Know More:

Q: The portion of a line intercepted between the coordinate axes is divided by the point (2,-1) in the ratio 3:2 . The equation of a line  is:

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