Question

Which of the following is the equation of the perpendicular bisector of the line segment joining the points X(2,4) and B(8,-2)?

Answer 1

step 1

Find out the slope of segment XB

m=(-2-4)/(8-2)

m=-6/6

m=-1

Remember that, if two lines are perpendicular, then their slopes are negative reciprocal

that means

the slope of the perpendicular bisector is

m=1

step 2

Find out the midpoint segment XB

$\begin{gathered} M(\frac{2+8}{2},\frac{4-2}{2}) \\ M(5,1) \end{gathered}$

step 3

Find out the equation of the perpendicular bisector

y=mx+b

we have

m=1

point M(5,1)

substitute and solve for b

1=(1)(5)+b

1=5+b

b=1-5

b=-4

therefore

the equation is

y=x-4