Answer:
C(7.2,0.7)
Step-by-step explanation:
Let point C be [tex]\frac{7}{10}[/tex] of the way from A to B, then [tex]AC:CB=7:3.[/tex]
If point [tex]C(x_C,y_C)[/tex] divides segment AB with endpoints [tex]A(x_A,y_A),\ B(x_B,y_B)[/tex] in the ratio [tex]m:n,[/tex] then
[tex]x_C=\dfrac{nx_A+mx_B}{m+n}\\ \\y_C=\dfrac{ny_A+my_B}{m+n}[/tex]
In your case, A(-4,-7) and B(12,4), so
[tex]x_C=\dfrac{3\cdot (-4)+7\cdot 12}{7+3}=\dfrac{-12+84}{10}=7.2\\ \\y_C=\dfrac{3\cdot (-7)+7\cdot 4}{7+3}=\dfrac{-21+28}{10}=0.7[/tex]
