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

##### 1 Answer

The other end is at

#### Explanation:

Write the equation of the perpendicular bisector in slope-intercept form,

The slope of the bisector is m = 1.

To find the slope of the bisected line, use the fact that the slopes of perpendicular are negative reciprocals of each other:

n = -1/m

Therefore, the slope of the bisected line is n = -1.

Use the slope-intercept form of the line,

b = 6

The equation of the bisected line is:

Because y = y, we can set the right side of equation [1] equal to the right side of equation [2]:

This means that the line segment starts at 2, ( which is

To find the corresponding y coordinate, substitute