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

Answer 1

#-2y-x=1# bisects line segments between #(8,3)# and any point on the line #-2y-x=16#

Consider a horizontal line segment from #(8,3)# extending to the left
with a total length twice that of the horizontal distance from #(8,3)# to the line #-2y-x=1#.
From the diagram below we can see that this horizontal line will intersect #-2y-x=1# at #(-7,3)#
and will have its left-most end at #(-22,3)#
#color(white)("XXX")rArr PR:RT = PQ:QS = 1:1#

#rArr QR# bisects #PT# for any point #T=(x',y')# on #-2y-x=16#

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Answer 2

Noah Atkinson

The other end of the line segment is at the point (5, -3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.