How do you find the equation for the perpendicular bisector of the segment with endpoints (-1,-3)(1,3) and (7,1)(7,1)?

1 Answer
May 18, 2018

y=-2x+5y=2x+5

Explanation:

"the perpendicular bisector bisects the line segment at"the perpendicular bisector bisects the line segment at
"right angles"right angles

"we require to find the midpoint of the segment and "we require to find the midpoint of the segment and
"the slope m"the slope m

"the midpoint of any endpoints say "(x_1,y_1)" and "(x_2,y_2)" is"the midpoint of any endpoints say (x1,y1) and (x2,y2) is

•color(white)(x)[1/2(x_1+x_2),1/2(y_1+y_2)]x[12(x1+x2),12(y1+y2)]

"midpoint "=[1/2(-1+7),1/2(-3+1)]midpoint =[12(1+7),12(3+1)]

color(white)("midpoint ")=[1/2(6),1/2(-2)]=(3,-1)midpoint =[12(6),12(2)]=(3,1)

"calculate slope m using the "color(blue)"gradient formula"calculate slope m using the gradient formula

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)xm=y2y1x2x1

"let "(x_1,y_1)=-1,-3)" and "(x_2,y_2)=(7,1)let (x1,y1)=1,3) and (x2,y2)=(7,1)

rArrm=(1-(-3))/(7-(-1))=4/8=1/2m=1(3)7(1)=48=12

"given a line with slope m then the slope of a line"given a line with slope m then the slope of a line
"perpendicular to it is"perpendicular to it is

•color(white)(x)m_(color(red)"perpendicular")=-1/mxmperpendicular=1m

rArrm_"perpendicular"=-1/(1/2)=-2mperpendicular=112=2

"the equation of a line in "color(blue)"point-slope form"the equation of a line in point-slope form is.

•color(white)(x)y-y_1=m(x-x_1)xyy1=m(xx1)

"where m is the slope and "(x_1,y_1)" a point on the line"where m is the slope and (x1,y1) a point on the line

"using "m=-2" and "(x_1,y_1)=(-1,-3)" then"using m=2 and (x1,y1)=(1,3) then

rArry+1=-2(x-3)larrcolor(red)"in point-slope form"y+1=2(x3)in point-slope form

rArry+1=-2x+6y+1=2x+6

rArry=-2x+5larrcolor(red)"in slope-intercept form"y=2x+5in slope-intercept form