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