A line segment is bisected by a line with the equation # - 3 y + 6 x = 6 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
The other end could be any point on the line
For convenience, I will rearrange the given equation
Consider the vertical line through
this vertical line will intersect
The distance between
Therefore one possible endpoint would be at
Perhaps less obviously, any point on a line through
will also be a line segment endpoint bisected by the given equation.
From the image above we can see that for an arbitrary point
(i.e. the given line is a bisector for
the line parallel to it and through
and using the slope-point form:
Which can be simplified as