ANSWER
[tex]x = \frac{ - 20}{7}[/tex]
[tex]y=\frac{ 4}{7}[/tex]
EXPLANATION
The 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]
Answer:
x = \frac{ - 20}{7}
y=\frac{ 4}{7}
Step-by-step explanation:
