A line segment is bisected by a line with the equation # 2 y + 9 x = 3 #. If one end of the line segment is at #(3 ,2 )#, where is the other end?
For a line with a slope that is perpendicular to the given line
Swap the coefficients of x and y, change the sign of one of the coefficients, and set it equal to an arbitrary constant:
To find the value of the constant, substitute the point
The equation of the bisected line is:
Multiply equation  by 9 and equation  by 2:
Add equation  to equation :
This is the x coordinate of intersection.
To find the corresponding y coordinate, substitute the value of