A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #( 8 , 1 )#, where is the other end?

1 Answer
sankarankalyanam
Oct 14, 2017

Coordinates of other end points (-6.6,3.6)

Explanation:

Assumption : Bisecting line is a perpendicular bisector

Standard form of equation #y=max+c#
Slope of perpendicular bisector m is given by
#3y-7x=2#
#y=(7/3)x+(2/3)#
#m=7/3#
Slope of line segment is
#y-1=-(1/m)(x-8)#
#y-1=-(3/7)(x-8)#
#7y-7=3x-24#

#7y-3x=-14color(white)((aaaa)# Eqn (1)
#3y-7x=2color(white)((aaaa)# Eqn (2)

Solving Eqns (1) & (2),
#21y-9x=42#
#21y-49x=14#
Subtracting and eliminating y term,
#40x=28#
#x=7/10#
Substituting value of x in Eqn (1),
#7y-(21/10)=14#
#y=(161/10)/7=23/10#
Mid point #(7/10,23/10)

Let (x1,y1) the other end point.
#(8+x1)/2=7/10#
#x1=-6.6#
#(1+y1)/2=23/10#
#y1=3.6#

Coordinates of other endpoint #(-6.6,3.6)#

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