Question

in what ratio does the point P(1,2) divide the join of A(-2,1) and B(7,4).​

Answer 1

Solution:

$\sf{By \ section \ formula} \\ \\ \boxed{\sf{x=\dfrac{mx_{2}+nx_{1}}{m+n}; \ y=\dfrac{my_{2}+ny_{1}}{m+n}}} \\ \\ \sf{Here, \ x=1, \ x_{1}=-2, \ x_{2}=7, \ y=2, \ y_{1}=1 \ y_{2}=4} \\ \\ \sf{\therefore{x=\dfrac{mx_{2}+nx_{1}}{m+n}}} \\ \\ \sf{\therefore{1=\dfrac{7m-2n}{m+n}}} \\ \\ \sf{\therefore{m+n=7m-2n}} \\ \\ \sf{\therefore{3n=6m}} \\ \\ \sf{\therefore{\dfrac{m}{n}=\dfrac{2}{1}}} \\ \\ \sf{\therefore{m:n=2:1}} \\ \\ \sf{Hence, \ P(1,2) \ divide \ line \ joining} \\ \\ \sf{A(-2,1) \ and \ B(7,4) \ in \ the \ ratio \ 2:1.}$