Answer:
(-2,2)
Step-by-step explanation:
If point C is located 3/5 of the way from point A to point B, then
AC : CB = 3 : 2
If point C divides segment AB in the ratio m : n, then its coordinates are
[tex]\left(\dfrac{nx_A+mx_B}{m+n},\dfrac{ny_A+my_B}{m+n}\right)[/tex]
In your case, points A and B have coordinates (4,5) and (-6,0), respectively. So, point C has coordinates
[tex]x_C=\dfrac{2\cdot 4+3\cdot (-6)}{3+2}=\dfrac{8-18}{5}=-2\\ \\y_C=\dfrac{2\cdot 5+3\cdot 0}{3+2}=\dfrac{10}{5}=2[/tex]
