Greetings from Brasil...
First we will calculate the distance between points A and B....
The expression that allows you to calculate the distance between two points is:
d(A; B) = √[(Xb - Xa)² + (Yb - Ya)²]
d(A; B) = √[(4 - (- 2))² + (3 - 0)²]
d(A; B) = √[6² + 3²]
d(A; B) = √45
45 = 3² · 5
d(A; B) = 3√5
L is 2/3 of the distance from AB, so
L = 2/3 · d(A; B)
L = 2/3 · 3√5
L = 2√5
For the coordinates of point L: let us use similarity of triangles...
BM/LN = AB/AL - refer to attached
3/Yl = 3√5/2√5
Yl = 2
As we can see in the graph, when Y = 2, X is also 2, so
L (2; 2)
there are other ways to accomplish this task
