Question

find the ratio in which the line segment joining the points (-3,10), and(6,-8) is divided by(-1,6)​

Answer 1

$\textbf{Given:}$

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

$\textbf{To find:}$

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

$\text{points (-3,10), and(6,-8) is divided by(-1,6)}$

$\textbf{Solution:}$

$\textbf{Section formula:}$

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

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

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

$\text{By using section formula,}$

$(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})=(-1,6)$

$(\dfrac{m(6)+n(-3)}{m+n},\dfrac{m(-8)+n(10)}{m+n})=(-1,6)$

$(\dfrac{6m-3n}{m+n},\dfrac{-8m+10n}{m+n})=(-1,6)$

$\implies\dfrac{6m-3n}{m+n}=-1$

$\implies\,6m-3n=-1(m+n)$

$\implies\,6m-3n=-m-n$

$\implies\,7m=2n$

$\implies\,\dfrac{m}{n}=\dfrac{2}{7}$

$\implies\boxed{\bf\,m:n=2:7}$

$\textbf{Answer:}$

$\textbf{(-1,6) divides the line segment joining (-3,10) and (6,-8) is 2:7}$

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.

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

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Answer 2

HIII MATE.... ur answer is attached...