# A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 1 , 4 )#, where is the other end?

##### 1 Answer

The other end of the line is at

#### Explanation:

Write the given line in slope-intercept form:

The slope,

Because the bisected line is perpendicular, we know that its slope, n, is the negative reciprocal of the bisector:

Use the given point,

The equation of the bisected line is:

Find the x coordinate of the intersection by subtracting equation [1] from equation [2]:

The x coordinate of the other end of the line is:

To find the corresponding y coordinate, substitute