(C) Let the $y$-axis divide the line segment joining $A(-3, -4)$ and $B(1, -2)$ in the ratio $k : 1$ at point $P(0, y)$.Using the section formula,the

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(C) Let the $y$-axis divide the line segment joining $A(-3, -4)$ and $B(1, -2)$ in the ratio $k : 1$ at point $P(0, y)$.Using the section formula,the $x$-coordinate of point $P$ is given by:$x = \frac{m x_2 + n x_1}{m + n}$Since the point lies on the $y$-axis,its $x$-coordinate is $0$:$0 = \frac{k(1) + 1(-3)}{k + 1}$$0 = k - 3$$k = 3$Therefore,the required ratio is $3 : 1$.

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

Easy

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

A
$1 : 3$
B
$2 : 3$
C
$3 : 1$
D
None of these

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Straight Line

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

If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

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Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

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What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

Medium

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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.

Medium

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The straight line $3x + y = 9$ divides the line segment joining the points $(1, 3)$ and $(2, 7)$ in the ratio

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

Similar Questions

If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

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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