A line segment starts at the point (2,3) and ends at the point (6,11). Find the equation of the perpendicular bisector of the segment. Demonstrate that your answer is correct. Your equation must be written in slope intercept form.

Mathematics · High School · Thu Feb 04 2021

llm

Answered on Sat Apr 16 2022

we know that when slope of line is m hen slope of perpendicular line is -1/m

now slope of line (2,3) and (6,11) is:-

m=y2-y1/x2-x1

where, x1=2 y1=3 x2=6 and y2=11 put these value in formula:-

m=11-3/ 6-2

m=8/4

m=2 (slope of plain line)

now slope of perpendicular line=-1/m

=-½

now coordinates of point that perpendicular bisect the line, that we can find by get mid point of line:-

let (a,b) are coordinates of perpendicular bisect line where, x=x1+x2/2 and y=y1+y2/2

x=2+6/2=8/2=4

y=3+11 /2=14/2=7

coordinates of point that perpendicular bisect the line are (4,7)

equation of line=> y-b=m(x-a)

y-7=-½(x-4)

y-7=-x/2+4/2

y=-x/2+4/2+7

y=-x/2+9

A line segment starts at the point (2,3) and ends at the point (6,11). Find the equation of the perpendicular bisector of the segment. Demonstrate that your answer is correct. Your equation must be written in slope intercept form.​