Answer:
C) y = -1/3x -1/3
Explanation:
You want the perpendicular bisector of the segment between the points (1, -4) and (3, 2).
Perpendicular bisector
The perpendicular bisector is the line perpendicular to the given segment that goes through the midpoint of the given segment. If the midpoint is ...
(h, k) = (x1 +x2, y1 +y2)/2
then the perpendicular bisector equation can be written ...
(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0
Application
The midpoint is ...
(h, k) = (1 +3, -4 +2)/2 = (4, -2)/2 = (2, -1)
The perpendicular line is ...
(3 -1)(x -2) +(2 -(-4))(y -(-1)) = 0
2x -4 +6y +6 = 0
Subtracting 6y and collecting terms, we have ...
2x +2 = -6y
Dividing by -6 puts this in the desired form:
y = -1/3x -1/3
__
Alternate solution
The slope of the segment is ...
m = (y2 -y1)/(x2 -x1) = (2 -(-4))/(3 -1) = 6/2 = 3
The slope of the perpendicular line is the opposite reciprocal of this: -1/3. As above the midpoint is (2, -1), so the point-slope equation is ...
y +1 = -1/3(x -2)
y = -1/3x +2/3 -1 . . . . subtract 1, eliminate parentheses
y = -1/3x -1/3