#"a perpendicular bisector, bisects a line segment at"#
#"right angles"#
#"to obtain the equation we require slope and a point on it"#
#"find the midpoint and slope of the given points"#
#"midpoint "=[1/2(1+5),1/2(4-2)]#
#color(white)("midpoint ")=(3,1)larrcolor(blue)"point on bisector"#
#"calculate the 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)=(1,4)" and "(x_2,y_2)=(5,-2)#
#rArrm=(-2-4)/(5-1)=(-6)/4=-3/2#
#"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/(-3/2)=2/3larrcolor(blue)"slope of bisector"#
#"using "m=2/3" and "(x_1,y_1)=(3,1)" then"#
#y-1=2/3(x-3)larrcolor(red)"in point-slope form"#
#rArry-1=2/3x-2#
#rArry=2/3x-1larrcolor(red)"in slope-intercept form"#
