A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #( 8 , 1 )#, where is the other end?
Coordinates of other end points (-6.6,3.6)
Assumption : Bisecting line is a perpendicular bisector
Standard form of equation
Slope of perpendicular bisector m is given by
Slope of line segment is
Solving Eqns (1) & (2),
Subtracting and eliminating y term,
Substituting value of x in Eqn (1),
Mid point #(7/10,23/10)
Let (x1,y1) the other end point.
Coordinates of other endpoint