Finding Images

Find the images of the triangle DCE under the following transformations: 1.Translation given by the vector u. 2. Line reflection given by the line a. 3. Rotation 90° clockwise about the point H 4. Glide reflection given by the line a and vector u. Make sure that you know how to do these by using a transparency and dynamic geometry software.

Application of isometries 1

Find the points B, C such that B is on the line b, C is on the line c and the triangle ABC is equilateral. How many solutions does the problem have?

Composition of Isometries 1

Point D is reflected about the line a. The image D' is then reflected about b and produces D''. Prove that the angle beta (blue) is twice the angle between the lines (alpha, green).

Rosette Pattern from a Generator

Generate a Rosette pattern based on the generator below. What is the symmetry of the resulting shape?