# A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?

##### 1 Answer

Any point on the line

#### Explanation:

Note that

The distance from

The distance from

Therefore the line segment from

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

Furthermore a line segment between

will also be bisected by

The equation of this line is

or

or, in a form similar to the given equation

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

See similar problem solution at:

https://socratic.org/questions/a-line-segment-is-bisected-by-a-line-with-the-equation-2-y-x-1-if-one-end-of-the#272239

for a more detailed solution with diagrams