Line m is the perpendicular bisector of segment AB. Write the equation of line m if the endpoints of the segment are A(-5, -2) and B(3, 4)

Answer 1

The perpendicular bisector of segment AB passes through its midpoint and has a slope that is the negative reciprocal of the slope of segment AB.

The midpoint of segment AB has coordinates:

([-5+3]/2, [-2,4]/2)

(-1, 1)

The slope of segment AB is:

slope = (4 - [-2])/(3 - [-5]) = 6/8 = 3/4

The slope of the perpendicular is therefore -4/3.

Using point-slope to write the equation for line m:

y - 1 = (-4/3)(x - [-1])

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

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

Here is a Desmos graph that shows all of the above:

desmos.com/calculator/pk96p9opck

Take a look to see how to name a point on Desmos and access its coordinates (x, y).

Answer 2

Slope AB = (4 - (-2)) / (3 - (-5)) = 3/4

So, slope of perp bisector is -1 / (3/4) = -4/3

Perpendicular bisector of AB contains the midpoint, M, of AB. M = ((-5+3)/2, (-2+4)/2) = (-1, 1)

Perpendicular bisectors equation has the form y = (-4/3)x + b.

Since (-1,1) is on the perp bisector, we have 1 = (-4/3)(-1) + b. So, b = -1/3.

Equation of perp bisector: y = (-4/3)x - 1/3.