How do you reflect a shape in a point?

Answer 1

Let's call the point of reflection O.

Take any point on the shape. Draw a line from that point to O and extend it beyond O for the same length (so that O is the midpoint of this line). The far end of the line is the image of the original point. Repeat for every point and you have the reflection of the original shape.

In actual fact, if the shape is a polygon, then you only need to reflect the vertices and join up their images. Well defined curves will form the same shape and it should not be too difficult to reproduce their reflection. However, with a random wriggly curve you have no choice but to map each point.