If the point (3, -4) divides the segment of t | vedclass

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Question

(A) Let the line intersect the $X$-axis at $(h, 0)$ and the $Y$-axis at $(0, k)$.Given that the point $(3, -4)$ divides the segment in the ratio $m :

Vedclass · Accepted Answer

$2x - y = 10$

Vedclass · Answer

(A) Let the line intersect the $X$-axis at $(h, 0)$ and the $Y$-axis at $(0, k)$.Given that the point $(3, -4)$ divides the segment in the ratio $m : n = 2 : 3$.Using the section formula: $(x, y) = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$.Substituting the values: $(3, -4) = \left(\frac{2(0) + 3(h)}{2+3}, \frac{2(k) + 3(0)}{2+3}\right)$.$(3, -4) = \left(\frac{3h}{5}, \frac{2k}{5}\right)$.Equating the coordinates: $3 = \frac{3h}{5} \Rightarrow h = 5$ and $-4 = \frac{2k}{5} \Rightarrow k = -10$.The intercept form of the line is $\frac{x}{h} + \frac{y}{k} = 1$.Substituting $h=5$ and $k=-10$: $\frac{x}{5} + \frac{y}{-10} = 1$.Multiplying by $10$: $2x - y = 10$.

If the point $(3, -4)$ divides the segment of the line between the $X$-axis and $Y$-axis in the ratio $2 : 3$,then the equation of the line is:

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