A line segment is bisected by a line with the equation # 4 y + 9 x = 8 #. If one end of the line segment is at #(5 ,2 )#, where is the other end?
The other end is at
Write the given line in slope-intercept form:
Because bisector is perpendicular, the slope of the line segment will be the negative reciprocal of its bisector,
This reference gives us an equation for the distance from the point to the line. The distance from the point to the line is:
The length of the line segment is twice this distance,
The other end of the line is at point: