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Sagot :
Answer:
The equation of the perpendicular bisector of the segment AB is [tex]y = x - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
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
[tex]-1m = -1[/tex]
[tex]m = 1[/tex]
So
[tex]y = x + b[/tex]
Passes through (4,2), which means that when [tex]x = 4, y = 2[/tex]. So
[tex]y = x + b[/tex]
[tex]2 = 4 + b[/tex]
[tex]b = -2[/tex]
So
[tex]y = x - 2[/tex]
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