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?
The other end is at
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  equal to the right side of equation :
This means that the line segment starts at 2, ( which is
To find the corresponding y coordinate, substitute