Problema Solution
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.
Answer provided by our tutors
let P(x, y) be the moving point and let M be the midpoint that lies on the line y=x
the coordinates of M are: M((1/2)(x+ 6), (1/2)(y + 0)) = M((1/2)(x+ 6), (1/2)y)
since M lies on y=x we have
(1/2)(x + 6) = (1/2)y multiply both sides by 2
x + 6 = y
the equation of the locus is y = x + 6.