Instructions on how to solve?

Graph the directed line segment ST with endpoints S(-3,-2) and T(4,5), Then find the coordinates of point P along the directed line segment ST so that the ratio of SP to PT is 3 to 4

P =  [ -3 + (3/7)(4 - -3),  -2 +(3/7)(5 - -2) ] =

[ -3 + (3/7)(7), -2 + (3/7)(7)]  =

[-3 + 3 , -2 +3 ]  =

[0, 1]

Proof

Distance from  S to T   sqrt[ 7^2 + 7^2] = sqrt(98)=  7sqrt(2)

Distance from  S to P   sqrt[ 3^2 + 3^2] =  sqrt(18)  =  3sqrt(2)

SP/ST  = 3sqrt(2) / 7sqrt(2)  =  3/7   →  PT/ST  =  4/7  ....so.....

SP/PT = 3 / 4