Question

if the point P (-3,2/3)lies in the line segment joining the points A (- 5 ,-4) and B (- 2,3) then. pls help me ​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\left(-3,\dfrac{2}{3}\right)\;lies\;in\;the\;line\;joining\;the}$

$\textsf{Points A(-5,-4) and B(-2,3)}$

$\underline{\textbf{To find:}}$

$\textsf{The ratio in which P divides line segment AB}$

$\underline{\textbf{Solution:}}$

$\textsf{Let P divides line segment AB internally in the ratio m:n}$

$\textsf{By section formula,}$

$\mathsf{\left(\dfrac{m\,x_2+n\,x_1}{m+n},\dfrac{m\,y_2+n\,y_1}{m+n}\right)=\left(-3,\dfrac{2}{3}\right)}$

$\mathsf{\left(\dfrac{m(-2)+n(-5)}{m+n},\dfrac{m(3)+n(-4)}{m+n}\right)=\left(-3,\dfrac{2}{3}\right)}$

$\mathsf{\left(\dfrac{-2m-5n}{m+n},\dfrac{3m-4n}{m+n}\right)=\left(-3,\dfrac{2}{3}\right)}$

$\textsf{Equating corresponding co-ordinates on bothsides,}$

$\mathsf{\dfrac{-2m-5n}{m+n}=-3}$

$\mathsf{-2m-5n=-3(m+n)}$

$\mathsf{-2m-5n=-3m-3n}$

$\mathsf{-2m+3m=5n-3n}$

$\mathsf{m=2\,n}$

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

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

$\therefore\textbf{P divides AB internally in the ratio 2:1}$

$\underline{\textbf{Find more:}}$

In what ratio does the x- axis divide the line segment joining A(5,6) and B (2,-8)?​  

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The point Q divides segment joining A (3, 5) and B (7, 9) in the ratio 2 : 3. Find the X-coordinate of Q.

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