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

1 Answer
Alan P.
Jun 1, 2016

Any point on the line -y+7x=-2

Explanation:

Note that (x,y)=(1,6) is a point on the line -y+7x=1#

The distance from (1,3) to (1,6) is 3

The distance from (1,3) to (1,6+3)=(1,9) is 6

(1,3), (1,6), and (1,9) are co-linear.

Therefore the line segment from (1,3) to (1,9) is bisected by the line -y+7x=1

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Furthermore a line segment between (1,3) and any point on a line through (1,9) parallel to -y+7x=1
will also be bisected by -y+7x=1

The equation of this line is
color(white)("XXX")y-9=7(x-1)
or
color(white)("XXX")y-7x=2
or, in a form similar to the given equation
color(white)("XXX")-y+7x=-2

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See similar problem solution at:
https://socratic.org/questions/a-line-segment-is-bisected-by-a-line-with-the-equation-2-y-x-1-if-one-end-of-the#272239
for a more detailed solution with diagrams

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