Question

Find the equation in point-slope form of the line that is the perpendicular bisector of the segment between (16,-4) and (-2,-76).

Answer 1

Given pair of points through the perpendicular line.

Equation of perpendicular line.

y+4 = 4(x-16)

y+4 = 4x-64

Subtract 4 from each side.

y = 4x-60

Slope of the above line is 4.

Required line slope is -1/4.

We don't know any point which is passes through the required line.

In this case we can't determine line equation.

Answer 2

End points of the segment are (16, - 4) and (- 2, - 76).

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

Let the points are (x₁, y₁) = (16, - 4) and (x₂, y₂) = (- 2, - 76).

Slope (m) = [(- 76 - (- 4))/(- 2 - 16)]

m = [( - 76 + 4)/(- 18)]

m  = [- 72/(- 18)]

⇒ m = 4.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular is - 1/4.

We need a point on the perpendicular bisector, to find this point we will find the midpoint of the two points.

Midpoint = [ (16 - 2)/2, (- 4 - 76)/2 ]
             = [ 14/2, - 80/2 ]

             = (7, - 40)

(x₁, y₁) = (7, - 40)

Point slope form of the line is y - y₁ = m(x - x₁)

The equation in point slope form is y + 40 = (- 1/4)( x - 7).