Question

Find an equation for the perpendicular bisector of the line segment whose endpointsare (-3, 2) and (7,6).

Answer 1

First, we need to find the midpoint. We can find it using the following equations:

`\begin{gathered} Mp=(xm,ym) \\ xm=(x1+x2)/(2) \\ ym=(y1+y2)/(2) \end{gathered}`

Where:

`\begin{gathered} (x1,y1)=(-3,2) \\ (x2,y2)=(7,6) \end{gathered}`

So:

`\begin{gathered} xm=(-3+7)/(2)=(4)/(2)=2 \\ ym=(6+2)/(2)=(8)/(2)=4 \end{gathered}`

Now, we need to find the slope of the line segment:

`m=(y2-y1)/(x2-x1)=(6-2)/(7-(-3))=(4)/(10)=(2)/(5)`

Since it is the line of the perpendicular bisector:

`\begin{gathered} m\cdot mb=-1 \\ (2)/(5)mb=-1 \\ mb=-(5)/(2) \end{gathered}`

Using the point-slope equation:

`\begin{gathered} y-ym=mb(x-xm_) \\ y-4=-(5)/(2)(x-2) \\ y-4=-(5)/(2)x+5 \\ y=-(5)/(2)x+9 \end{gathered}`

Answer:

`y=-(5)/(2)x+9`