Idon’t understand how this is solved

Here in such type of problems we will say that for the equilibrium of rod torque as well as net force must be balanced

So first we will use the torque balance on the rod about the hinge point

we know that length of the rod is L = 5 m

now by solving above

now we also know that

now by force balance in Y direction

now force balance in X direction

now the net reaction force is given as

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

where are the vectors ?