Determine the ratio in which the line 2x + y | vedclass

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Question

(A) Let the line $2x + y - 4 = 0$ divide the line segment joining $A(2, -2)$ and $B(3, 7)$ in the ratio $k:1$.Using the section formula,the coordinate

Vedclass · Accepted Answer

$2:9$

Vedclass · Answer

(A) Let the line $2x + y - 4 = 0$ divide the line segment joining $A(2, -2)$ and $B(3, 7)$ in the ratio $k:1$.Using the section formula,the coordinates of the point of division are $\left(\frac{3k + 2}{k + 1}, \frac{7k - 2}{k + 1}\right)$.Since this point lies on the line $2x + y - 4 = 0$,we substitute these coordinates into the equation:$2\left(\frac{3k + 2}{k + 1}\right) + \left(\frac{7k - 2}{k + 1}\right) - 4 = 0$Multiplying by $(k + 1)$,we get:$2(3k + 2) + (7k - 2) - 4(k + 1) = 0$$6k + 4 + 7k - 2 - 4k - 4 = 0$$9k - 2 = 0$$9k = 2$$k = \frac{2}{9}$Thus,the required ratio is $2:9$.

Determine the ratio in which the line $2x + y - 4 = 0$ divides the line segment joining the points $A(2, -2)$ and $B(3, 7)$.

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