Question

Write the equation for the perpendicular bisector of the given line segment.

A
B)
4.3x+ /
= 3x }

Answer 1

`y=(1)/(3)x+(5)/(3)`

Explanation:

Let

A(-5,5),B(-2,-4) ----> the given segment

step 1

Find the slope AB

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

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

substitute the given values

`m=(-4-5)/(-2+5)`

`m=(-9)/(3)`

`m=-3`

step 2

we know that

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

so

the slope of the perpendicular bisector is equal to

`m_1*m_2=-1`

we have

`m_1=-3`

substitute

`(-3)*m_2=-1`

`m_2=(1)/(3)`

step 3

Find the midpoint segment AB

A(-5,5),B(-2,-4)

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

`M((x1+x2)/(2) ,(y1+y2)/(2))`

substitute the values

`M((-5-2)/(2) ,(5-4)/(2))`

`M(-(7)/(2) ,(1)/(2))`

step 4

Find the equation of the line in point slope form

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

we have

`m=(1)/(3)`

`M(-(7)/(2) ,(1)/(2))`

substitute

`y-(1)/(2)=(1)/(3)(x+(7)/(2))`

step 5

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y-(1)/(2)=(1)/(3)x+(7)/(6)`

`y=(1)/(3)x+(7)/(6)+(1)/(2)`

`y=(1)/(3)x+(10)/(6)`

simplify

`y=(1)/(3)x+(5)/(3)`

see the attached figure to better understand the problem