Answer:
y = x -4
Explanation:
A perpendicular bisector of a line AB will pass through the midpoint of the line AB
AB is a line segment between A(3, -3) and B(1, -1)
Midpoint of AB is the average of the x and y coordinates of A and B
Let M be the midpoint
x coordinate of M = (3 + 1)/2 = 4/2 = 2
y coordinate of M = (-3 + (-1))/2 = -4/2 = -2
So M is at point (2, -2)
The slope of line AB can be determined as follows
Slope = (yb - ya)/(xb-xa) where (xa, ya) and (xb, yb) are coordinates of points A and B respectively
Slope of AB = (-1 - (-3)/(1 -3 = (-1 + 3) /(1 -3 ) = 2/-2 = -1
A line which is perpendicular to AB will have slope which is negative of the reciprocal of slope of AB
Slope of AB = -1
Reciprocal of slope AB = 1/-1 = -1
Negative of this reciprocal = 1
So perpendicular line will be of the form
y = 1x + b where b is the y intercept
Since this is a perpendicular bisector it has to pass through M(2, -2)
Substitute y = -2 and x = 2 to solve for b
-2 = 1(2) + b
-2 = 2 + b
-4 = b
b = -4
So the equation of the perpendicular bisector is y = x -4