Question

A line segment has endpoints at (4, –6) and (0, 2).

What is the slope of the given line segment?


What is the midpoint of the given line segment?


What is the slope of the perpendicular bisector of the given line segment?


What is the equation, in slope-intercept form, of the perpendicular bisector?

Answer 1

Slope of segment: (−6 − 2)/(4 − 0) = −8/4 = −2.

Midpoint: ((4+0)/2, (−6+2)/2) = (2, −2).

Slope of perpendicular bisector: negative reciprocal of −2 is 1/2.

Equation (point-slope through (2, −2)): y + 2 = (1/2)(x − 2) ⇒ y = (1/2)x − 3.