Exam 11: The Mathematics of Symmetry: Beyond Reflection

-Consider the diagram shown below; triangle XYZ undergoes a translation along a vector V resulting in the image of point X being located at point Q. What are the (,x y) coordinates of the image of point Z under a translation along the same vector V?

Consider the diagram from problem 1; what are the (,x y) coordinates of the image of point Q under a 90° clockwise rotation with rotocenter A?

How many reflection symmetries does the following object have?

Consider the diagram from problem 1; triangle XYZ undergoes a translation along a vector V resulting in the image of point Z being located at point R. What are the (,x y) coordinates of the Image of point Y under a translation along the same vector V?

Classify the border pattern shown below by its symmetry type. Use the standard crystallographic notation (mm, mg, m1, 1m, 1g, 12 or 11).

-Consider the diagramshown above ; triangle XYZ undergoes a translation along a vector V resulting in its image of point Y being located at point R. What are the (,x y) coordinates of the image of point X under a translation along the same vector V?

Consider the diagram shown below. Triangle ABC has been mapped to triangle A'B'C' using a single rigid motion. What type of rigid motion was done to complete this mapping?

Classify the border pattern shown below by its symmetry type. Use the standard crystallographic notation (mm, mg, m1, 1m, 1g, 12 or 11).

What is the symmetry type of the object shown below?

What is the symmetry type of the object shown below?

Consider the diagram from problem 1; what are the (x,y) coordinates of the image of point S under a 180° clockwise rotation with rotocenter A?

-Consider the diagram shown below; what are the (,x y) coordinates of the image of point Y under a 180° clockwise rotation with rotocenter A?

Consider the diagram from problem 1; under a glide reflection with axis l1 , triangle XYZ is mapped so that the image of point X is point S. What are the (,x y) coordinates of the image of point Z under this same glide reflection?

Consider the diagram shown below. What are the (,x y) coordinates of the image of point R under a reflection with axis l1 ?

-Consider the diagram shown above ; under a glide reflection with axis l1 , triangle XYZ is mapped so that the image of point X is point S. What are the (,x y) coordinates of the image of point Y under this same glide reflection?

Consider the diagram from problem 1; triangle XYZ undergoes a translation along a vector V resulting in the image of point X image being located at point P. What are the (,x y) coordinates of the image of point Z under a translation along the same vector V?

Classify the border pattern shown below by its symmetry type. Use the standard crystallographic notation ( mm, mg}, m1,1m, 1g, 12 or 11 ).

Including the identity symmetry, how many rotation symmetries does the following object have?

What is the symmetry type of the object shown below?

Consider the diagram shown below. Triangle ABC has been mapped to triangle A'B'C' using a single rigid motion. What type of rigid motion was done to complete this mapping?