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
Any point on the line
Explanation:
Note that
The distance from
The distance from
Therefore the line segment from
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Furthermore a line segment between
will also be bisected by
The equation of this line is
or
or, in a form similar to the given equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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