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Math Problem Frogs Jump Symmetry Axis
Proved as follows:

Suppose the coordinates of four points are (Ax, Ay). (Bx,By),? (Cx, Cy) and (Px, Py)

(1)P is symmetric about a, and the coordinate of P 1 is (2Ax-Px,? 2Ay-Py)

(2)P 1 is symmetric about b, and the P2 coordinate is (2Bx-(2Ax-Px). 2By-(2Ay-Py))? =? (2Bx-2Ax+Px,? 2By-2Ay+Py)

(3)P2 is symmetric about C, and P3 is (2Cx-(2Bx-2Ax+Px). 2Cy-(2By-2Ay+Py))? =? (2Cx-2Bx+2Ax-Px,? 2Cy-2By+2Ay-Py)

(4)P3 is symmetric about a, and P4 is (2Ax-(2Cx-2Bx+2Ax-Px). 2Ay-(2Cy-2By+2Ay-Py))? =? (-2Cx+2Bx+Px,? -2Cy+2By+Py)

(5)P4 is symmetric about B, and the coordinate of P5 is (2Bx-(-2Cx+2Bx+Px). 2By-(-2Cy+2By+Py))? =? (2Cx-Px,? 2Cy-Py)

(6)P5 is symmetric about C, and P6 coordinates are (2Cx-(2Cx-Px),? 2Cy-(2Cy-Py))? =? (Px,? Py)

If ABC and P are on the four vertices of a square, only three steps are needed.