The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3). What are the x- and y-coordinates of point M, which partitions the directed line segment into the ratio 2:5?x = y =

ANSWER[tex]x = \frac{ - 20}{7}[/tex][tex]y=\frac{ 4}{7}[/tex]EXPLANATIONThe x and y coordinates of the point that partition [tex](x_1,y_1)[/tex]and[tex](x_2,y_2)[/tex]in the ratio m:n is given by:[tex]x = \frac{mx_{2} + nx_{1}}{m + n} [/tex]and[tex]y= \frac{my_{2} + ny_{1}}{m + n} [/tex]The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3).We substitute the given points,[tex]x_1=-6[/tex][tex]y_1=2[/tex][tex]x_2=5[/tex][tex]y_2=-3[/tex][tex]m = 2[/tex][tex]n = 5[/tex]This implies that;[tex]x = \frac{2(5)+ 5( - 6)}{2 + 5} [/tex][tex]x = \frac{10 - 30}{2 + 5} [/tex][tex]x = \frac{ - 20}{7} [/tex][tex]y = \frac{2( - 3)+ 5( 2)}{2 + 5} [/tex][tex]y = \frac{ - 6+ 10}{2 + 5} [/tex][tex]y=\frac{ 4}{7}[/tex]