# A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?

##### 1 Answer

Any point on the line

or

if the given line **perpendicular** bisector then

#### Explanation:

Apology:

Even omitting some details, this explanation is quite long.

Consider the vertical line

This vertical line will intersect

A point twice as far above

That is the line segment from

Furthermore, as we can see from similar triangles any line parallel to

so any line parallel to it must also have a slope of

and

if such a line passes through

or simplified as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

It is possible, since this question was asked under the heading "Perpendicular Bisectors" that it was intended that

In this case the perpendicular line to

would have a slope of

an equation of

The system of equations:

can be solved for the point of intersection: