Math 3210 Quiz #4 Fall 2006

(a) Write the equations for the glide reflection which consists of a reflection about the

line x = 3 followed by a translation by the vector (0, 5).
(b) Find the inverse of this glide reflection and write it's equations.

Solution:

(a) To get the equation for the reflection, first translate the line x = 3 to the y-axis by the translation given by

x'' = x – 3 and y '' = y.

Now, reflect about the y-axis to get

x"' = -x'' = 3 - x and y"' = y'' = y.

Finally translate the y-axis back to the line x = 3,

x' = x''' + 3 = 6 - x and y' = y''' = y.

Now the translation is given by

x' = x and y' = y + 5

therefore the composition is :

x' = 6-x and y' = y + 5.

(b) To obtain the inverse, solve the above equations for x and y to get

x = 6-x' and y = y' - 5

Thus the inverse is given by

x' = 6-x and y' = y - 5.