Answer
The coordinates of the point P are (-2,2)
Step-by-step explanation:
We can use the formula
[tex]P=\left(\frac{x_{1}+rx_{2}}{1+r}, \frac{x_{2}+ry_{2}}{1+r}\right)[/tex]
Where [tex]A=(x_{1},y_{2}), B={x_{2},y_{2}}[/tex] and [tex]r[/tex] is the desired ratio. On our case we have [tex]r=\frac{1}{3}, A=(-5,4), B=(7,-4)[/tex]. Then replacing in the formula we have
[tex]P=\left(\frac{-5+7\cdot \frac{1}{3}}{1+1/3},\frac{4+(-4)\cdot \frac{1}{3}}{1/3}\right)=(-2,2).[/tex]
