15. As shown in the figure, put a rectangular piece of paper OABC in a plane rectangular coordinate system, make OA and OC fall on the X axis and Y axis respectively, connect OB, and fold the paper OABC along OB, so that point A falls on the position of A'. If OB= root 5, BC/OC= 1/2, find the coordinate of point A' as _.

OA=BC= 1, AB=OC=2 can be found from the valley theorem; Let the coordinate of A' be (x, y), then because A and A' are symmetrical about the straight line OB, the midpoint of AA' must be on OB (that is, the straight line Y=2X), and the equation 1:

Y/2=2*(X+ 1)/2

besides

According to Pythagorean theorem, X2+Y2=OA'2=OA2= 1.

Just solve this set of equations.