Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 1 , 1 ) (−1,1) and ( − 7 , − 7 ) (−7,−7).?

Answer 1

`y=-3/4x-6`

Explanation:

.

End points of the line segment:

`(-1,1) and (-7,-7)`

The slope of the line is:

`m_1=(y_2-y_1)/(x_2-x_1)=(-7-1)/(-7-(-1))=(-8)/(-7+1)=(-8)/(-6)=4/3`

The slope of a line perpendicular to this line segment, `m_2`, can be found from the following equation:

`m_1m_2=-1`

`4/3m_2=-1`

`m_2=(-1)/(4/3)=(-1)(3/4)=-3/4`

Let's find the midpoint of the line segment:

`((x_1+x_2)/2,(y_1+y_2)/2)=((-1+(-7))/2,(1+(-7))/2)=((-8)/2,(-6)/2)=(-4,-3)`

Now, we can write the equation of a straight line that goes through `(-4,-3)` and has a slope of `m_2=-3/4`, which is in the form of `y=mx+b`:

`y=-3/4x+b`

`b` is the `y`-intercept of the line and can be found by plugging in the coordinates of the point it goes through:

`-3=-3/4(-4)+b`

`-3=3+b`

`b=-6`

Therefore, the equation of the perpendicular bisector is:

`y=-3/4x-6`