Question

Find the ratio in which line segment joining (-3,10) and (6,-8) is divided by y axis also find the point of division

Answer 1

Step-by-step explanation:

Given that: Find the ratio in which line segment joining (-3,10) and (6,-8) is divided by y axis also find the point of division.

To find: Ratio in which Y-Axis divides the line segment

Solution:

To find the ratio ,

let us assume that Y-Axis divides line segment of joining of A(-3,10) and B(6,-8) in k:1.

As we know that section Formula

$\bold{x = \frac{mx_2 + nx_1}{ m+ n}} \\ \\ \bold{y = \frac{my_2 + ny_1}{ m+ n}}$

Thus,coordinates of intersection point

$x = \frac{6k - 3}{k + 1}...eq1 \\ \\ y = \frac{ - 8k + 10}{k + 1} ...eq2$

On every point of y-axis ,x coordinate is zero.

so,put eq1 equal to zero

$0 = \frac{6k - 3}{k + 1} \\ \\ 6k - 3 = 0 \\ \\ 6k = 3 \\ \\ k = \frac{3}{6} \\ \\ \bold{\blue{\frac{k}{1} = \frac{1}{2}}}$

Thus,

Y-Axis divides the line segment in 1:2.

To find point of division

put value of k in y coordinate

$y = \frac{ - 8k + 10}{k + 1} \\\\y= \frac{ - 8\big(\frac{1}{2}\big)+ 10}{\big(\frac{1}{2}\big) + 1}\\\\y=\frac{12}{3}\\\\y=4$

Coordinate of intersection point

(0,4)

Hope it helps you.

Answer 2

$\textbf{Given:}$

$\text{Points (-3,10) and (6,-8) }$

$\textbf{To find:}$

$\text{The ratio in which line segment joining the given points is}$

$\text{divided by y axis}$

$\textbf{Solution:}$

$\textbf{Section formula:}$

$\text{The co ordinates of the point which divides the}$

$\text{line segment joining (x_1,y_1) and (x_2,y_2) internally in the ratio m:n are}$

$\boxed{\bf(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})}$

$\text{Let the given points be A(-3,10) and B(6,-8)}$

$\text{Let P be the point on y axis which divides line joining A and B}$

$\text{internally in the ratio m:n}$

$\text{Then, coordinates of P are}$

$(\dfrac{m(6)+n(-3)}{m+n},\dfrac{m(-8)+n(10)}{m+n})$

$(\dfrac{6m-3n}{m+n},\dfrac{-8m+10n}{m+n})$

$\text{Since P lies on y axis, its x coordinate is zero}$

$\dfrac{6m-3n}{m+n}=0$

$6m-3n=0$

$6m=3n$

$\dfrac{m}{n}=\dfrac{3}{6}$

$\dfrac{m}{n}=\dfrac{1}{2}$

$\implies\boxed{\bf\,m:n=1:2}$

$\text{Also,}$

$P\,(\dfrac{1(6)+2(-3)}{1+2},\dfrac{1(-8)+2(10)}{1+2})$

$P\,(\dfrac{6-6}{3},\dfrac{-8+20}{3})$

$P\,(\dfrac{0}{3},\dfrac{12}{3})$

$P\,(0,4)$

$\textbf{Answer:}$

$\textbf{y axis divides the line joining A and B in the ratio 1:2}$

$\textbf{Point of division is (0,4)}$

Find more:

In what ratio is the line segment joining A(2,-3)&B(5,6) divided by x-axis also find the coordinate of the point of division.

https://brainly.in/question/7118881

Find the ratio in which the line segment joining the points (- 2 3) and (3 - 2) is divided by y axis​

https://brainly.in/question/14355682