To write the equation for the perpendicular bisector of a segment, you need to know the slope of the segment and its midpoint.
The midpoint is the average of the end coordinates.
((-6+6)/2, (-2+4)/2) = (0/2, 2/2) = (0, 1)
The slope of the line between the endpoints is the y difference divided by the x difference.
M = (4-(-2))/(6-(-6)) = 6/12 = 1/2
Your line has a slope that is the negative reciprocal of this, -1/(1/2) = -2.
The point-slope form of the equation for the line is
y-y1 = m(x-x1)
We have (x1, y1) = (0, 1), so the line is
y-1 = -2(x-0)
Adding 1 to both sides of the equation gives
The midpoint is the average of the end coordinates.
((-6+6)/2, (-2+4)/2) = (0/2, 2/2) = (0, 1)
The slope of the line between the endpoints is the y difference divided by the x difference.
M = (4-(-2))/(6-(-6)) = 6/12 = 1/2
Your line has a slope that is the negative reciprocal of this, -1/(1/2) = -2.
The point-slope form of the equation for the line is
y-y1 = m(x-x1)
We have (x1, y1) = (0, 1), so the line is
y-1 = -2(x-0)
Adding 1 to both sides of the equation gives