Right Bisector Line Seg

Question

Determine the equation of the right bisector of the line segment E(2, 6) and F(4, -2). Draw the diagram?

Answer 1

Find the midpoint of the line segment:

midpoint = ((2+4)/2 , (6-2)/2)) = (3, 2)

 

The bisector will go through (3, 2)

The slope will be perpendicular to the line segment

so it meets at a right angle.

The slope of EF is (-2-6)/(4-2) = -8/2 = -4

The slope of the perpendicular is the negative

reciprocal or (-1)/(-4) = 1/4

 

The perpendicular bisector of EF has

slope 1/4 and goes through (3, 2)

 

Use point slope formula

y-y₁ = m(x-x₁)

 

y - 2 = (1/4)(x-3)

 

Work that equation to standard format or

slope intecept form.