(A) Let the ratio be $k : 1$. The point of intersection with the $x$-axis has a $y$-coordinate of $0$.Using the section formula for the $y$-coordinate

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(A) Let the ratio be $k : 1$. The point of intersection with the $x$-axis has a $y$-coordinate of $0$.Using the section formula for the $y$-coordinate: $y = \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2}$.Setting $y = 0$,we get $0 = \frac{k(6) + 1(-4)}{k + 1}$.This implies $6k - 4 = 0$,so $6k = 4$,which gives $k = \frac{4}{6} = \frac{2}{3}$.Thus,the ratio is $2 : 3$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

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

A
$2 : 3$
B
$2 : 3$
C
$3 : 2$
D
$2 : 3$

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System of co-ordinates, Distance between two points, Section formulae

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

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