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

1 Answer
May 18, 2018

y=-2x+5

Explanation:

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

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

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

•color(white)(x)[1/2(x_1+x_2),1/2(y_1+y_2)]

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

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

"let "(x_1,y_1)=-1,-3)" and "(x_2,y_2)=(7,1)

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

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

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

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

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

•color(white)(x)y-y_1=m(x-x_1)

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

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

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

rArry+1=-2x+6

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