"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"
