The coordinates of the endpoints of directed line segment ABC are A(-8,7) and C(7,-13). If AB:BC = 3:2, the coordinates of B are

Answer:The coordinates of B are (1,-5).Step-by-step explanation:To find the coordinates of point [tex]B[/tex] we will apply section formula.Its used to find out if any line segment is of any [tex]m_1: m_2[/tex] ratios.As the lie segment is joining the points internally we will use section formula for internal points.Lets say that [tex]B[/tex] is having coordinates [tex](k,l)[/tex] then [tex]k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}[/tex] and [tex]l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}[/tex]Now we have [tex]A=(8,7)[/tex] we call it [tex](x_1,y_1)[/tex] then [tex]C=(7,-13)[/tex] we call it [tex](x_2,y_2)[/tex].And [tex]m_1=3[/tex],[tex]m_2=2[/tex]Plugging all the values in section formula we have.[tex]k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}[/tex][tex]k=\frac{3(7) +2(-8)}{2+3}[/tex] [tex]= \frac{21-16}{5}= 1[/tex]Similarly [tex]l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}[/tex][tex]l=\frac{3(-13) +2(7)}{2+3}[/tex][tex]l=\frac{-39+14}{5}= -5[/tex]So the coordinates of [tex]B =(1,-5)[/tex]