Question

The ratio in which the point $P(\frac{3}{4},\frac{5}{12})$ divides the line segment joining the points A$(\frac{1}{2},\frac{3}{2})$ and B (2,-5) is 1:5
If true then enter $1$ and if false then enter $0$

Answer 1

$LetapointP(x,y)=(\frac{3}{4},\frac{5}{12})dividethelinesegmentABjoiningthepointsA(x_1,y_1)=(\frac{1}{2},\frac{3}{2})\&B(x_2,y_2)=(2,-5)intheratiom:n.Then,bythesectionformula,x=\frac{n{x}_2+m{x}_1}{m+n}.substitutingforx,x_1\&x_{2}weget\therefore \frac{m\times 2+n\times \frac{1}{2}}{m+n}=\frac{3}{4}.⟹16m+4n=6m+6n⟹\frac{m}{n}=\frac{1}{5}i.em:n=1:5Wegetthesameresultifweconsidery=\frac{n{y}_1+m{y}_2}{m+n}\&proceedintheaboveway.Ans-m:n=1:5.$