Question

the coordinates of the endpoints of AB are A (-8, -2) and B(16,6). Point P is on AB what are the coordinates of point P such that AP:PB is 3:5?

Answer 1

We have that
A (-8, -2) and B(16,6)

step 1
find the distance AB in the x coordinates
dABx=(16-(-8))-----> 24 units

step 2
find coordinate x of P (Px)
Px=Ax+(3/5)*dABx------> Px=(-8)+(3/5)*24----> 6.4

step 3
Find the distance AB in the y coordinates
dABy=(6-(-2))-----> 8 units

step 4
find coordinate y of P (Py)
Py=Ay+(3/5)*dABy------> Py=(-2)+(3/5)*8----> 2.8

the coordinates of P are (6.4,2.8)

see the attached figure