Solution
Since it is a perpendicular bisector, hence point M is the midpoint
[tex]\begin{gathered} \therefore Mid\text{ point AB}=(\frac{-2+5}{2},\frac{7+2}{2}) \\ mid\text{ point=(}\frac{3}{2},\frac{9}{2}) \end{gathered}[/tex]
Slope
[tex]\text{Slope (m)=}\frac{2-7}{5--2}=-\frac{5}{7}[/tex]
Since they are perpendicular
[tex]\begin{gathered} m_1\times m_2=-1 \\ -\frac{5}{7}\times m_2=-1 \\ m_2=\frac{7}{5} \end{gathered}[/tex]
The equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-5=\frac{7}{5}(x-2) \\ y-5=\frac{7}{5}x-\frac{14}{5} \\ y=\frac{7}{5}x-\frac{14}{5}+5 \\ y=\frac{7}{5}x+\frac{11}{5} \end{gathered}[/tex]
The final answer
[tex]y=\frac{7}{5}x+\frac{11}{5}[/tex]
