(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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Straight Line

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

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $x$-axis.

Medium

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If the polar coordinates of a point are $(2, \pi /3)$,find its Cartesian coordinates.

Easy

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The points which trisect the line segment joining the points $(0, 0)$ and $(9, 12)$ are

Medium

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The inclination of the straight line passing through the point $(-3, 6)$ and the midpoint of the line joining the points $(4, -5)$ and $(-2, 9)$ is

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If the polar coordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

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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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Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $x$-axis.

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