Point A is at (3,4) and point B is at (8, -4). What is the midpoint of line segment AB?

(5.5, 0 )

Step-by-step explanation:

Given points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

The midpoint of A(3, 4) and B(8, - 4) is therefore

[ 0.5(3 + 8), 0.5(4 - 4) ] = (5.5, 0 )

Step 1

Find the slope of the line M

we have

isolate the variable y

the slope of the line is

Step 2

Find the slope of the line perpendicular to line M

we know that

if two lines are perpendicular , then the product of their slopes are equal to minus one

so

we have

Find m2

therefore

the answer is