Question

M and N are the two points on x axis and y axis repetitively P=(3,2) devide the line segment MN in ratio 2:3 find the coordinate of M and N and slope of line MN

Answer 1

$\underline{\textsf{Given :}}$

$\textsf{M and N are the two points on x axis and y axis and}$

$\textsf{P(3,2) divides MN in the ratio 2:3}$

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

$\textsf{co-ordinates of M and N and slope of MN}$

$\underline{\textsf{Solution :}}$

$\textsf{Since M and N are the points on x axis and y axis, we can write}$

$\textsf{M(x,0) and N(0,y)}$

$\textsf{By section formula,we get}$

$\mathsf{(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})=(3,2)}$

$\mathsf{(\dfrac{2(0)+3(x)}{2+3},\dfrac{2(y)+3(0)}{2+3})=(3,2)}$

$\mathsf{(\dfrac{3x}{5},\dfrac{2y}{5})=(3,2)}$

$\textsf{Equating corresponding coordinates}$

$\mathsf{\dfrac{3x}{5}=3\;\;\&\;\;\dfrac{2y}{5}=2}$

$\mathsf{x=5\;\;\&\;\;y=5}$

$\therefore\boxed{\textsf{M(5,0)\;\;\&\;\;N(0,5)}}$

$\textsf{Now,}$

$\textsf{Slope of MN}$

$\mathsf{=\dfrac{y_2-y_1}{x_2-x_1}}$

$\mathsf{=\dfrac{5-0}{0-5}}$

$\mathsf{=\dfrac{5}{-5}}$

$\mathsf{=-1}$

$\therefore\boxed{\textsf{Slope of MN}=-1}$

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