First, we need to find the midpoint. We can find it using the following equations:
[tex]\begin{gathered} Mp=(xm,ym) \\ xm=\frac{x1+x2}{2} \\ ym=\frac{y1+y2}{2} \end{gathered}[/tex]
Where:
[tex]\begin{gathered} (x1,y1)=(-3,2) \\ (x2,y2)=(7,6) \end{gathered}[/tex]
So:
[tex]\begin{gathered} xm=\frac{-3+7}{2}=\frac{4}{2}=2 \\ ym=\frac{6+2}{2}=\frac{8}{2}=4 \end{gathered}[/tex]
Now, we need to find the slope of the line segment:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}[/tex]
Since it is the line of the perpendicular bisector:
[tex]\begin{gathered} m\cdot mb=-1 \\ \frac{2}{5}mb=-1 \\ mb=-\frac{5}{2} \end{gathered}[/tex]
Using the point-slope equation:
[tex]\begin{gathered} y-ym=mb(x-xm_) \\ y-4=-\frac{5}{2}(x-2) \\ y-4=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+9 \end{gathered}[/tex]
Answer:
[tex]y=-\frac{5}{2}x+9[/tex]
