find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-4,-8), B(0,0) ; 3 to 1

Answer:The coordinate of point P along the directed line segment AB is ( - 1 , - 2 )Step-by-step explanation:Given as :The coordinate of the points A = ( - 4 , - 8 )The coordinate of the points B = ( 0 , 0 )The Point P divide the line joining points A and B in the ratio m : n = 3 : 1Let The coordinates of the points P = ( x , y )So, x = [tex]\dfrac{mx_2 + nx_1}{m + n}[/tex]And y = [tex]\dfrac{my_2 + ny_1}{m + n}[/tex]∴  x =  [tex]\dfrac{mx_2 + nx_1}{m + n}[/tex]Or, x = [tex]\frac{3\times 0+1\times (-4)}{3 + 1}[/tex]Or, x = [tex]\frac{0-4}{4}[/tex]∴   x = - 1Similarly     y =  [tex]\dfrac{my_2 + ny_1}{m + n}[/tex]Or, y = [tex]\frac{3\times 0+1\times (-8)}{3 + 1}[/tex]Or, y = [tex]\frac{0-8}{4}[/tex]∴   y = - 2so, coordinate of P ( x , y ) = ( - 1 , - 2 )Hence The coordinate of point P along the directed line segment AB is     ( - 1 , - 2 )  Answer