Answer:
The coordinates of the point C are:
             (8.5,-6)
Step-by-step explanation:
We know that if a point C(x,y) divides the line segment A(a,b) B(c,d) in the ratio m:n then the coordinates of point C are given by:
[tex]x=\dfrac{m\times c+n\times x}{m+n}\ ,\ y=\dfrac{m\times d+n\times b}{m+n}[/tex]
Here we have:
m=3 and n=1
a=4 , b=3 , c=10 and d= -9
Hence, we have:
[tex]x=\dfrac{3\times 10+1\times 4}{3+1}\ ,\ y=\dfrac{3\times (-9)+1\times 3}{3+1}\\\\x=\dfrac{30+4}{4}\ ,\ y=\dfrac{-27+3}{4}\\\\x=\dfrac{34}{4}\ ,\ y=\dfrac{-24}{4}\\\\x=8.5\ ,\ y=-6[/tex]
Hence, the coordinates of the point C are:
           (8.5,-6)
