Find the ratio in which the y-axis divides th | vedclass

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

Question

(A) Let the ratio in which the $y$-axis divides the line segment be $k:1$.By the section formula,the coordinates of the point dividing the segment joi

Vedclass · Accepted Answer

Ratio $5:1$,Point $(0, -13/3)$

Vedclass · Answer

(A) Let the ratio in which the $y$-axis divides the line segment be $k:1$.By the section formula,the coordinates of the point dividing the segment joining $(x_1, y_1) = (5, -6)$ and $(x_2, y_2) = (-1, -4)$ in the ratio $k:1$ are given by:$\left( \frac{kx_2 + x_1}{k+1}, \frac{ky_2 + y_1}{k+1} \right) = \left( \frac{k(-1) + 5}{k+1}, \frac{k(-4) + (-6)}{k+1} \right) = \left( \frac{-k+5}{k+1}, \frac{-4k-6}{k+1} \right)$.Since this point lies on the $y$-axis,its $x$-coordinate (abscissa) must be $0$.Therefore,$\frac{-k+5}{k+1} = 0$,which implies $-k+5 = 0$,so $k = 5$.Thus,the ratio is $5:1$.Now,substitute $k=5$ into the $y$-coordinate expression:$y = \frac{-4(5) - 6}{5+1} = \frac{-20-6}{6} = \frac{-26}{6} = -\frac{13}{3}$.Hence,the point of intersection is $(0, -13/3)$.

Find the ratio in which the $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also,find the point of intersection.

Similar Questions

Let $A(4, 2), B(6, 5)$ and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of the centroid of the triangle.

Find the values of $y$ for which the distance between the points $P(2, -3)$ and $Q(10, y)$ is $10$ units.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-1,-2), (1,0), (-1,2), (-3,0)$.

Determine if the points $(1,5), (2,3),$ and $(-2,-11)$ are collinear.

Find the area of the quadrilateral whose vertices,taken in order,are $(-4,-2), (-3,-5), (3,-2),$ and $(2,3)$ (in square units).

Vedclass Test Series

Exam Paper Generator

Online Exam Module