In what ratio does the x-axis divide the line | vedclass

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(A) Let the $x$-axis divide the line segment joining the points $A(3, 4)$ and $B(5, 6)$ in the ratio $k:1$ at point $P(x, 0)$.Using the section formul

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$ - \frac{2}{3} $

Vedclass · Answer

(A) Let the $x$-axis divide the line segment joining the points $A(3, 4)$ and $B(5, 6)$ in the ratio $k:1$ at point $P(x, 0)$.Using the section formula,the $y$-coordinate of point $P$ is given by:$y = \frac{m_1y_2 + m_2y_1}{m_1 + m_2}$Since the point lies on the $x$-axis,its $y$-coordinate is $0$.$0 = \frac{k(6) + 1(4)}{k + 1}$$0 = 6k + 4$$6k = -4$$k = -\frac{4}{6} = -\frac{2}{3}$Thus,the ratio is $-2:3$ or $-\frac{2}{3}$.

In what ratio does the $x$-axis divide the line segment joining the points $(3, 4)$ and $(5, 6)$?

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