Question

Find the equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)

Answer 1

Since it is a perpendicular bisector, hence point M is the midpoint

`\begin{gathered} \therefore Mid\text{ point AB}=((-2+5)/(2),(7+2)/(2)) \\ mid\text{ point=(}(3)/(2),(9)/(2)) \end{gathered}`

Slope

`\text{Slope (m)=}(2-7)/(5--2)=-(5)/(7)`

Since they are perpendicular

`\begin{gathered} m_1* m_2=-1 \\ -(5)/(7)* m_2=-1 \\ m_2=(7)/(5) \end{gathered}`

The equation of the perpendicular bisector of the line AB with A(-2,7) and B(5,2)

`\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-5=(7)/(5)(x-2) \\ y-5=(7)/(5)x-(14)/(5) \\ y=(7)/(5)x-(14)/(5)+5 \\ y=(7)/(5)x+(11)/(5) \end{gathered}`

The final answer

`y=(7)/(5)x+(11)/(5)`