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Think of any figure, with any shape, on the graph with the origin inside the shape.

Now think of any point inside the shape (except the origin).

Now, in your imagination, slowly and carefully turn the shape 180 degrees around the origin ...

as if it were stuck to the origin with a pin, and you gave it 1/2 turn on the pin.

What happened to the point you were thinking of ?

If the point started out some distance to the right of the y-axis, it wound up the same distance

to the left of the y-axis.

And if it started out some distance above the x-axis, it wound up the same distance below the x-axis.

So ... any point that starts out at the coordinates ( x , y ) before the 1/2 turn, winds up

at the coordinates ( -x , -y ) after the 1/2 turn.

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Q: How do you find the coordinates of a figure when it is rotated 180 degrees around the origin?
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