A line segment is bisected by a line with the equation # 5 y -4 x = 1 #. If one end of the line segment is at #(3 ,8 )#, where is the other end?
The other end is at the point
It is implied that the bisector is perpendicular to bisected line, therefore we can use the slope of the bisector to find the slope of the bisected line.
Write the equation of the bisector line in slope-intercept form so that we may observe the slope:
The slope, n, of the bisected line is the negative reciprocal,
Substitute the slope and the point,
The equation of the bisected line is:
Subtract equation  from equation :
The x coordinate of intersection is:
The point of intersection is 2 units to the right of the starting point; the ending point must be an additional 2 units:
Substitute 7 for x into equation :