Answer:
The coordinates of point B are (-3,-3).
Step-by-step explanation:
Let [tex]A(x,y) = (6,-6)[/tex], [tex]C(x,y) = (-6,-2)[/tex] and [tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex], then we have the following formula by vectorial definition of a line segment:
[tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex]
[tex]B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)][/tex]
[tex]B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)[/tex]
[tex]B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)[/tex]
[tex]B(x,y) = (-3, -3)[/tex]
