A perpendicular bisector cuts a line segment in half at a 90-degree angle.
To find the perpendicular bisector, find the midpoint of the lines and the negative reciprocal. Finally, Plug these into the equation for a line in slope-intercept form.
(3,-1) = (x1,y1)
(-3,5) = (x2,y2)
Apply midpoint formula
[tex]midpoint=\text{ (}\frac{x1+x2}{2},\frac{y2+y1}{2})\text{ = }\frac{3-3}{2},\frac{-1+5}{2}=(0,2)[/tex]find the slope (m)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-(-1)}{-3-3}=\frac{6}{-6}=-1[/tex]Negative reciprocal of the slope:
-1 =1
Slope intercept form:
y=mx+b
Where:
m= slope
b= y-intercept
Put the negative reciprocal of the slope in the equation:
y= 1x+b
y=x+b
Plug the points of the midpoint into the line, and solve for b
Midpoint (0,2)
2=0+b
2=b
Final equation:
y= x+2
