We can use the segment formula to solve this. The formula is:
Where m and n are in the ratio.
x_1, x_2, y_1, and y_2 are the respective coordinates.
Given m = 1 and n = 3
A(3,6)
B(7,-10)
Now, we plug it into formula and get out coordinates of C:
[tex]\begin{gathered} (x,y)=(\frac{1(6)+3(3)}{1+3},\frac{1(-10)+3(7)}{1+3}) \\ =(\frac{6+9}{4},\frac{-10+21}{4}) \\ =(\frac{15}{4},\frac{11}{4}) \end{gathered}[/tex]The Coordinates of C are:
[tex]C=(\frac{15}{4},\frac{11}{4})[/tex]
