I have a problem related to triangles. Please give me some hint to progress.
Suppose we have the following coordinates $A(-2,3)$,$B(1,-1)$,$C(-1,-1)$. From point $A$, draw a line which divides the area of triangle $ABC$ in the ratio $1:2$.
I have calculated the length of the sides: $[AB]=5$,$[AC]=\sqrt{17}$ and $[BC]=2$.
I have searched online for what this line should be, like medians, altitudes or etc and found this, where is written:
If one median of a triangle is drawn, the second median to be drawn will divide the areas of the two triangles formed by the first median in the ratio 1:2.
But is it what I need? I can write the equation of lines which go through $AC$,$BC$,$AB$, but how do I find the equation of the required line?