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(B) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The coordinates of the points are $A(a, 0)$ and $B(0, b)$

Vedclass · Accepted Answer

$8x - 5y + 60 = 0$

Vedclass · Answer

(B) Let the intercepts of the line on the $x$-axis and $y$-axis be $a$ and $b$ respectively. The coordinates of the points are $A(a, 0)$ and $B(0, b)$.Given that the point $P(-5, 4)$ divides the line segment $AB$ in the ratio $1 : 2$.Using the section formula,the coordinates of $P$ are given by $\left( \frac{1 \cdot 0 + 2 \cdot a}{1 + 2}, \frac{1 \cdot b + 2 \cdot 0}{1 + 2} \right) = \left( \frac{2a}{3}, \frac{b}{3} \right)$.Equating the coordinates,we get $\frac{2a}{3} = -5 \implies a = -\frac{15}{2}$ and $\frac{b}{3} = 4 \implies b = 12$.The intercept form of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values,we get $\frac{x}{-15/2} + \frac{y}{12} = 1 \implies -\frac{2x}{15} + \frac{y}{12} = 1$.Multiplying by $60$,we get $-8x + 5y = 60$,which simplifies to $8x - 5y + 60 = 0$.

The intercept of a line between the coordinate axes is divided by the point $(-5, 4)$ in the ratio $1 : 2$. The equation of the line will be:

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