In what ratio does the x-axis divide the line | vedclass

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

Question

(A) Let the $x$-axis divide the line segment joining the points $A(3, 4)$ and $B(5, 6)$ in the ratio $k:1$ at point $P(x, 0)$.Using the section formul

Vedclass · Accepted Answer

$ - \frac{2}{3} $

Vedclass · Answer

(A) Let the $x$-axis divide the line segment joining the points $A(3, 4)$ and $B(5, 6)$ in the ratio $k:1$ at point $P(x, 0)$.Using the section formula,the $y$-coordinate of point $P$ is given by:$y = \frac{m_1y_2 + m_2y_1}{m_1 + m_2}$Since the point lies on the $x$-axis,its $y$-coordinate is $0$.$0 = \frac{k(6) + 1(4)}{k + 1}$$0 = 6k + 4$$6k = -4$$k = -\frac{4}{6} = -\frac{2}{3}$Thus,the ratio is $-2:3$ or $-\frac{2}{3}$.

In what ratio does the $x$-axis divide the line segment joining the points $(3, 4)$ and $(5, 6)$?

Similar Questions

Find the coordinates of the point which divides the line segment joining the points $(1, -2, 3)$ and $(3, 4, -5)$ in the ratio $2:3$ externally.

If the orthocenter and circumcenter of a triangle are $(3, -4, 2)$ and $(2, 1, 3)$ respectively,then its centroid is

Find the ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, -8)$ is divided by the $YZ$-plane.

Using the section formula,show that the points $A(2, -3, 4)$,$B(-1, 2, 1)$,and $C(0, \frac{1}{3}, 2)$ are collinear.

Find the coordinates of the centroid of the triangle whose vertices are $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})$ and $(x_{3}, y_{3}, z_{3})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module