# A line segment is bisected by a line with the equation # - 2 y - x = 1 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?

##### 1 Answer

#### Explanation:

Consider a horizontal line segment from

with a total length twice that of the horizontal distance from

From the diagram below we can see that this horizontal line will intersect

and will have its left-most end at

Obviously this horizontal line is bisected by

Consider a line through this left-most point with the same slope as

Using the slope-point form we can see that the equation of this line can be written as

**Assertion**

for any point

This Assertion follows immediately from considering a modified version of the above diagram.

Since