Question

For the given line segment, write the equation of the perpendicular bisector.

Answer 1

`y=-0.8x-4.7`

Explanation:

Let

`A(-6,-4), B(-2,1)`

we know that

The perpendicular bisector pass through the midpoint of AB

step 1

Find the midpoint AB

`M=((-6-2)/2,(-4+1)/2)`

`M=(-4,-1.5)`

step 2

Find the slope of the given line AB

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(1+4)/(-2+6)`

`m=(5)/(4)`

step 3

Find the slope of the perpendicular bisector

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

`m1*m2=-1`

we have

`m1=(5)/(4)` ----> slope of the given line

substitute in the formula

`(5)/(4)*m2=-1`

`m2=-(4)/(5)=-0.8`

step 4

Find the equation of the perpendicular bisector

we know that

The equation of the line into point slope form is equal to

`y-y1=m(x-x1)`

we have

`m=-0.8`

`M=(-4,-1.5)`

substitute

`y+1.5=-0.8(x+4)`

`y=-0.8x-3.2-1.5`

`y=-0.8x-4.7`