Because vector AP= 1/2 vector PB

So (-5-x, 4-0)= 1/2(0-(-5), y-4).

That is -5-x=( 1/2)*5.

4=y-4

X=- 15/2 y=8。

So a (-15/2,0) b (0,8)

Given point A and point P, the equation is solved by two-point formula.

Or know points p and b, and solve the linear equation with two-point formula.