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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(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 $:1$)?

Similar Questions

If the centroid of $\Delta ABC$ is $G(3, 3)$ and the vertices are $B(-1, 2)$ and $C(2, -3)$,then find the area of $\Delta ABC$.

If the distance between the points $(a, 1)$ and $(8, a)$ is $5,$ then $a=$

The distance of the point $P(2, 3)$ from the $x$-axis is

The triangle with the vertices $(0,0)$,$(4.2,0)$,and $(0,9.1)$ is a $\ldots \ldots \ldots$ triangle.

If $(-8, -4), (-2, 4)$ and $(5, a)$ are collinear points,then find the value of $a$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module