ANSWER
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
EXPLANATION
We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.
The x-coordinate of this point is given by:
[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]
[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]
[tex]x= \frac{21 - 12}{4 + 3} [/tex]
[tex]x= \frac{9}{7} [/tex]
The y-coordinates is given by;
[tex]y= \frac{my_2+ny_1}{m + n} [/tex]
[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]
[tex]y= \frac{39+12}{4 + 3}[/tex]
[tex]y= \frac{51}{7}[/tex]
Hence
[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]
