In which ratio does the Y-axis divide the lin | vedclass

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(A) Let the $Y-$axis divide the line segment $AB$ at point $P(0, y)$ in the ratio $k:1$. Using the section formula, the coordinates of point $P$ are g

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$4$

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(A) Let the $Y-$axis divide the line segment $AB$ at point $P(0, y)$ in the ratio $k:1$. Using the section formula, the coordinates of point $P$ are given by: $P = \left( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} \right)$ Here, $m_1 = k$, $m_2 = 1$, $(x_1, y_1) = (-4, 1)$, and $(x_2, y_2) = (1, 1)$. Since the point lies on the $Y-$axis, its $x-$coordinate is $0$: $0 = \frac{k(1) + 1(-4)}{k + 1}$ $0 = k - 4$ $k = 4$ Thus, the ratio is $4:1$.

In which ratio does the $Y-$axis divide the line segment joining $A (-4, 1)$ and $B (1, 1)$ from $A$ (in $:1$)?

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