Question #eed1a

1 Answer
Feb 28, 2018

#y=-3/2x+9#

Explanation:

#"we require to find the slope m and midpoint M of the"#
#"given line segment"#

#"to calculate m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(8,10)" and "(x_2,y_2)=(-4,2)#

#rArrm=(2-10)/(-4-8)=(-8)/(-12)=2/3#

#"the slope of the perpendicular bisector is therefore"#

#•m_(color(red)"perpendicular")=-1/m=-1/(2/3)=-3/2#

#M=[1/2(8-4),1/2(10+2)]=(2,6)#

#"equation of bisector with "m=-3/2" and "#
#(x_1,y_1)=(2,6)#

#y-6=-3/2(x-2)#

#rArry=-3/2x+9larrcolor(red)"perpendicular bisector"#