Explanation:
The complete question is shown in the attached file. We know that:
[tex]J(x_{1},y_{1})=J(-15,-5) \\ \\ K(x_{2},y_{2})=K(25,15) \\ \\ \\ m:n=1:4 \\ \\ \\ So: \\ \\ m=1 \\ \\ n=4[/tex]
From the formulas:
[tex]x=\left(\frac{m}{m+n}\right)(x_{2}-x_{1})+x_{1} \\ \\ \\ Substituting \ values: \\ \\ x=\left(\frac{1}{1+4}\right)(25-(-15))-15 \\ \\ x=\left(\frac{1}{5}\right)(40)-15 \\ \\ x=8-15 \\ \\ x=-7[/tex]
[tex]y=\left(\frac{m}{m+n}\right)(y_{2}-y_{1})+y_{1} \\ \\ \\ Substituting \ values: \\ \\ y=\left(\frac{1}{1+4}\right)(15-(-5))-5 \\ \\ y=\left(\frac{1}{5}\right)(20)-5 \\ \\ y=4-5 \\ \\ y=-1[/tex]
Finally:
[tex]\boxed{E(-7,-1)}[/tex]
