SOLUTION: 26.) The midpoint of the line segment joining a moving point to (6,0) is on the line y=x. Find the equation of its locus. Ans. x-y+6=0 This is a question that comes with the

Graph the line :



Call point (6,0) the point R.

Draw an arbitrary line from point R(6,0), crossing the
line  at point M, and extending to P so that MP
equals RM. making M the midpoint of RP.  P is the moving
point.



Label the moving point P with the variable coordinates (x,y) 



Since point M is the midpoint of the line segment RP, we use
the midpoint formula to label M with the coordinates 
(,) or (,) 



Now the point M(,) is on the line , so
it must satisfy the equation , so we substitute that point 
into the equation  and we get:



Multiply both sides by 2:



That is equivalent to



To see the path of the moving point we draw the graph of
 in green




Edwin