# 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?

##### 1 Answer

The general line containing all the endpoints of line segments with other endpoint

The endpoint of the *perpendicular* bisector is

#### Explanation:

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

We have

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:

Check: