denote the vector from point X to point Y.
Let P be a point in the plane of triangle ABC.
What is the
locus of points
Q as P traces the triangle ABC ?
(In reply to Solution?
When P moves from (0,0) to (xb,yb), PQ does indeed go from (xb+xc,yb+yc) to (xc-2*xb,yc-2*yb).
However, PQ is a vector; it isn't the point Q. The vector takes the point P, now at (xb, yb), to the point Q at (xc-xb,yc-yb), and so the traced line of Q for this segment is from (xb+xc,yb+yc) to (xc-xb,yc-yb), and thus is twice (not three times) the length of the segment traced by P.
Symmetry shows that if it were three times, the opposite vertex would fall 1/3 of the way along the generated segment; but 1/3 from which direction? ... there's no asymmetry to favor one or the other.
Posted by Charlie
on 2008-05-15 17:16:20