In what ratio does the line 3x + 4y = 7 divid | vedclass

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Question

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

Vedclass · Accepted Answer

$4:9$

Vedclass · Answer

(A) Let the line $3x + 4y - 7 = 0$ divide the segment joining $A(1, 2)$ and $B(-2, 1)$ in the ratio $k:1$.Using the section formula,the coordinates of the point of division are $\left( \frac{-2k + 1}{k+1}, \frac{k + 2}{k+1} \right)$.Since this point lies on the line $3x + 4y = 7$,we substitute these coordinates into the equation:$3\left( \frac{-2k + 1}{k+1} \right) + 4\left( \frac{k + 2}{k+1} \right) = 7$$3(-2k + 1) + 4(k + 2) = 7(k + 1)$$-6k + 3 + 4k + 8 = 7k + 7$$-2k + 11 = 7k + 7$$4 = 9k$$k = \frac{4}{9}$Thus,the ratio is $4:9$.

In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

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