Answer:
The equation of the perpendicular bisector of the segment AB is
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
In which m is the slope and b is the y-intercept.
Perpendicular lines and slopes:
If two lines are perpendicular, the multiplication of their slopes is -1.
Equation of the perpendicular bisector of the segment AB.
Equation of a line that passes through the midpoint of segment AB and is perpendicular to AB.
Midpoint of segment AB:
Mean of their coordinates x and y. So
(1+7)/2 = 4
(5-1)/2 = 2
So (4,2).
Slope of segment AB:
When we have two points, the slope between them is given by the change in y divided by the change in x.
In segment AB, we have points (1,5) and (7,-1). So
Change in y: -1 - 5 = -6
Change in x: 7 - 1 = 6
Slope: -6/6 = -1
Equation of the perpendicular bisector:
The slope, multiplied with the slope of segment AB, is -1. So
So
Passes through (4,2), which means that when . So
So