A line segment is bisected by a line with the equation # 9 y - 2 x = 5 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?
The general line containing all the endpoints of line segments with other endpoint
The endpoint of the perpendicular bisector is
If the line is the perpendicular bisector of the segment, the other endpoint is uniquely determined.
If the line is just a bisector, as asked, each point on the line is the bisector of some segment whose endpoint is
If we're told
The other endpoint
That's parallel to the original line, as far from it as
Now let's ask which
The direction of the segment is
We have perpendicularity when the dot product is zero: