We are given one endpoint (2, 5) and a midpoint (5, 1)
We are asked to find the coordinates of the other endpoint
Recall that the midpoint formula is given by
[tex]\mleft(x_m,y_m\mright)=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]Where
[tex](x_m,y_m)=(5,1)_{}\text{ and }(x_1,y_1)=(2,5)[/tex]So, the other endpoint can be found as
[tex]x_m=\frac{x_1+x_2}{2},y_m=\frac{y_1+y_2}{2}[/tex]Substitute the known values
[tex]\begin{gathered} 5=\frac{2_{}+x_2}{2},\text{ }1_{}=\frac{5_{}+y_2}{2} \\ 2\times5=2_{}+x_2,\text{ }2\times1_{}=5_{}+y_2 \\ 10=2_{}+x_2,\text{ }2_{}=5_{}+y_2 \\ x_2=10-2,\text{ }y_2=2-5 \\ x_2=8,\text{ }y_2=-3 \end{gathered}[/tex]Therefore, the coordinates of the other endpoint are
[tex](x_2,y_2)=(8,-3)[/tex]