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Find an equation for the perpendicular bisector of the line segment whose endpoints are ( − 2 , − 1 ) (−2,−1) and ( − 6 , − 5 ) (−6,−5)?

Answer 1

Maverick Smith

#y=-x-7#

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

#"we require to find the midpoint of the segment and it's"# #"slope"#

#"given "(x_1,y_1)" and "(x_2,y_2)" then the midpoint is"#

#[1/2(x_1+x_2),1/2(y_1+y_2)]#

#"here "(x_1,y_1)=(-2,-1)" and "(x_2,y_2)=(-6,-5)#

#"midpoint "=[1/2(-2-6),1/2(-1-5)]=(-4,-3)#

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

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"to calculate m use the "color(blue)"gradient formula"#

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

#"let "(x_1,y_1)=(-2,-1)" and "(x_2,y_2)=(-6,-5)#

#m=(-5-(-1))/(-6-(-2))=(-4)/(-4)=1#

#"slope of perpendicular "=-1/m=-1#

#y=-x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-4,-3)" into the partial"#

#"equation"#

#-3=4+brArrb=-3-4=-7#

#y=-x-7larrcolor(red)"perpendicular bisector"#

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