# A line segment is bisected by a line with the equation # 4 y + x = 3 #. If one end of the line segment is at #(5 ,6 )#, where is the other end?

##### 1 Answer

The other end is at

#### Explanation:

Given the equation of the perpendicular bisector of the form:

The equation of the bisected line is of the form:

Writing the equation of the given perpendicular bisector in the above form:

Now, we can with the general form for the bisected line:

To find the value of

The equation of the bisected line is:

Find the point of intersection of the lines:

Multiply the second equation by 4 and add to the first equation:

Solve for x:

Use the given line to solve for y:

We can use the midpoint equations to find the other end:

Substitute

Solve for

The other end is at