If the line 2x + y = k passes through the poi | vedclass

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(B) Let the points be $A(1, 1)$ and $B(2, 4)$. The point $P(x, y)$ divides $AB$ in the ratio $m:n = 3:2$.Using the section formula,$x = \frac{mx_2 + n

Vedclass · Accepted Answer

$7/5$

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(B) Let the points be $A(1, 1)$ and $B(2, 4)$. The point $P(x, y)$ divides $AB$ in the ratio $m:n = 3:2$.Using the section formula,$x = \frac{mx_2 + nx_1}{m+n} = \frac{3(2) + 2(1)}{3+2} = \frac{6+2}{5} = \frac{8}{5}$.$y = \frac{my_2 + ny_1}{m+n} = \frac{3(4) + 2(1)}{3+2} = \frac{12+2}{5} = \frac{14}{5}$.The point $P$ is $(\frac{8}{5}, \frac{14}{5})$.Since the line $2x + y = k$ passes through $P$,we substitute the coordinates of $P$ into the equation:$2(\frac{8}{5}) + \frac{14}{5} = k \implies \frac{16}{5} + \frac{14}{5} = k \implies k = \frac{30}{5} = 6$.Now,we need to find the ratio $(k+1):(k-1)$.Substituting $k=6$,we get $(6+1):(6-1) = 7:5$.Thus,the value is $\frac{7}{5}$.

If the line $2x + y = k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ internally in the ratio $3:2$,then $(k+1):(k-1) =$

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