Question

The coordinates of the endpoints of ab are A(-6,-5) and b(4,0). Point p is on ab. Determine and state the coordinates of point p, such that AP:PB is 2:3

Answer 1

we have that
A(-6,-5) and B (4,0)

we know that
AP:PB is 2:3
so
(2+3)=5
AP=2/5
PB=3/5

step 1
find the x coordinate of P
Px=Ax+AP*ABx
where
Ax is the x coordinate of A
AP is 2/5
ABx is the distance AB in the x coordinate
so
PX=[-6+(2/5)*(4+6)]------>Px=-2

step 2
find the y coordinate of P
Py=Ay+AP*ABy
where
Ay is the y coordinate of A
AP is 2/5
ABy is the distance AB in the y coordinate
so
Py=[-5+(2/5)*(0+5)]------>Py=-3

the point P is (-2,-3)

see the attached figure