# 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?

##### 1 Answer

The other end could be any point on the line

#### Explanation:

For convenience, I will rearrange the given equation

as

Consider the vertical line through

Since

this vertical line will intersect

The distance between

The point

Therefore

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

and since

(i.e. the given line is a bisector for

Since

the line parallel to it and through

and using the slope-point form:

Which can be simplified as