Question

If the intercept of a line between the coordinate axes is divided by the point (–5 4) in the ratio 1 : 2, then find the equation of the line.

Answer 1

If the intercept of a line between the coordinate axes is divided by the point (–5 4) in the ratio 1 : 2, then find the equation of the line is

8x - 5y + 60 = 0

Step-by-step explanation:

Let the line meets the coordinate axes at (a, 0) and (0, b) respectively

Thus the intercept of the line on the coordinate axes will be a, b

And the equation of the line will be

$\boxed{\frac{x}{a}+\frac{y}{b}=1}$   (Intercept form of equation of line)

It is given that point (-5, 4) divided line joining (a, 0) and (0, b) in the ratio 1:2

We know that if $(x, y)$ divides the line joining $(x_1,y_1)$ and $(x_2, y_2)$ in the ratio $m_1:m_2$ then

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

And,

$\boxed{y=\frac{m_1y_2+m_2y_1}{m_1+m_2}}$

Thus,

$-5=\frac{1\times 0+2\times a}{1+2}$

$\implies -5=\frac{2a}{3}$

$\implies a=-\frac{15}{2}$

Similarly

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

$\implies b=12$

Therefore, the equation of the line is

$\frac{x}{(-15/2)}+\frac{y}{12}=1$

$\implies -\frac{2x}{15}+\frac{y}{12}=1$

$\implies -\frac{8x}{60}+\frac{5y}{60}=1$

$\implies -8x+5y=60$

$\implies 8x-5y+60=0$

This is the required equation of the line.

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Answer 2

Answer:

8x-5y+60=0

Step-by-step explanation:

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