#"we require the slope and midpoint of the endpoints"#
#"the midpoint is the average of the coordinates of"#
#"the endpoints"#
#"midpoint "=[1/2(3-1),1/2(7-5)]=(1,1)#
#"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)=(3,7)" and "(x_2,y_2)=(-1,-5)#
#rArrm=(-5-7)/(-1-3)=(-12)/(-4)=3#
#"the slope of a perpendicular line to this is"#
#•color(white)(x)m_(color(red)"perpendicular")=-1/m#
#rArrm_(color(red)"perpendicular")=-1/3#
#"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=-1/3x+blarrcolor(blue)"is partial equation"#
#"to find b substitute "(1,1)" into the partial equation"#
#1=-1/3+brArrb=4/3#
#rArry=-1/3x+4/3larrcolor(red)"is perpendicular bisector"#
