LM has the endpoints L at –5 and M at 9. To find the point x so that x divides the directed line segment LM in a 2:3 ratio, use the formula x = (x2 – x1) + x1.x = (9 – (–5)) + (–5)

Answer:The value of point x is [tex]\frac{3}{5}[/tex].Step-by-step explanation:It is given that LM has the endpoints L at –5 and M at 9.The point x divides the directed line segment LM in a 2:3 ratio.The given formula is[tex]x=\frac{m}{m+n}(x_2-x_1)+x_1[/tex]Using above formula we get[tex]x=\frac{2}{2+3}(9-(-5))+(-5)[/tex][tex]x=\frac{2}{5}(9+5)-5[/tex][tex]x=\frac{2}{5}(14)-5[/tex][tex]x=\frac{28}{5}-5[/tex][tex]x=\frac{28-25}{5}[/tex][tex]x=\frac{3}{5}[/tex]Therefore the value of point x is [tex]\frac{3}{5}[/tex].