The line segment joining the points (2, -3) a | vedclass

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Question

(A) Let the ratio in which the $y$-axis divides the line segment joining the points $(x_1, y_1) = (2, -3)$ and $(x_2, y_2) = (-5, 6)$ be $k : 1$.The c

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$2 : 5$

Vedclass · Answer

(A) Let the ratio in which the $y$-axis divides the line segment joining the points $(x_1, y_1) = (2, -3)$ and $(x_2, y_2) = (-5, 6)$ be $k : 1$.The coordinates of the point of division on the $y$-axis are given by $\left( \frac{kx_2 + x_1}{k+1}, \frac{ky_2 + y_1}{k+1} \right)$.Since the point lies on the $y$-axis,its $x$-coordinate must be $0$.Therefore,$\frac{k(-5) + 2}{k+1} = 0$.$-5k + 2 = 0 \implies 5k = 2 \implies k = \frac{2}{5}$.Thus,the required ratio is $2 : 5$.

The line segment joining the points $(2, -3)$ and $(-5, 6)$ is divided by the $y$-axis in the ratio:

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