Wie finden Sie die Gleichung der senkrechten Winkelhalbierenden der Punkte # (1,4) # und # (5, -2) #?

#"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"#