#"the perpendicular bisector, bisects the segment at "#

#"right angles"#

#"mid-point "=[1/2(-1+(-7)),1/2(2+0)]#

#color(white)(xxxxxxxx)=(-4,1)#

#"given a line with slope m then the slope of a line "#

#"perpendicular to it is"#

#m_(color(red)"perpendicular")=-1/m#

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(-1,2)" and "(x_2,y_2)=(-7,0)#

#rArrm=(0-2)/(-7-(-1))=(-2)/(-6)=1/3#

#rArrm_(color(red)"perpendicular")=-1/(1/3)=-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"#

#rArry=-3x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-4,1)" into the partial equation"#

#1=12+brArrb=-11#

#"equation of perpendicular bisector is"#

#y=-3x-11larrcolor(red)"in slope-intercept form"#