# A line segment is bisected by a line with the equation # - 4 y + x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?

##### 1 Answer

The other end is at

#### Explanation:

Let's write the given line in the form

The general equation of lines perpendicular to this line is:

To find the value of c, substitute 7 for x and 2 for y:

The equation of the bisected line segment is:

The midpoint is at the intersection of of these two lines:

Multiply equation [1] by 4 and subtract from equation [2]

Let

The y coordinate of the other end of the line,

To find the corresponding x coordinate, substitute

The other end is at

Here is a graph of two lines and two points: