Answer to Question #249219 in Analytic Geometry for jls

Question

find the coordinates of the point L that divides segment MN into a ratio of ML:LN to 1:3; M(-4,0) and N(0,4). Write your answer in coordinate form (x,y)

Answer 1

Let the coordinates of point $L$ be $(x,y).$

Given that $ML:LN$ is $1:3$ .

Using section formula, we get:

$(x,y)=(\frac{-12+0}{4},\frac{0+4}{3})\\ \therefore x=-3,y=\frac{4}{3}$

So, coordinates of point $L$ be $(-3,\frac{4}{3}).$