One way to represent how an isometry (or any other transformation of space) transforms the plane (or any space) is through analytic geometry:[br][br](A) Introduce a coordinate system in the plane[br](B) Identify points, P, in the plane by their coordinates: P(x,y)[br](C) Specify the coordinates for the new point, P', to which P is mapped by the isometry: P'(x',y').[br][br]So the isometry is represented by the mapping P(x,y)-->P'(x',y'). [br][br]Use the applet below to determine where the point, P(x,y), is mapped by the following isometries:[br][br]1) Reflection over any of the lines of reflection shown in the applet;[br]2) Rotation about the origin by 90 degrees or 180 degrees;[br]3) Translation in any direction.