12.1.4 Compositions of Transformations

Question 1

composition of transformations

Answer 1

one transformation followed by another

Question 2

glide transformation

Answer 2

the composition of a translation and a reflection across a line parallel to the translation vector

Question 3

Theorem

Answer 3

composition of two isometries is an isometry

Question 4

Theorem

Answer 4

The composition of two reflections across two parallel lines is equivalent to a translation.
• The translation vector is perpendicular to the lines.
• The length of the translation vector is twice the distance between the lines.
The composition of two reflections across two intersecting lines is equivalent to a rotation.
• The center of rotation is the intersection of the lines.
• The angle of rotation is twice the measure of the angle formed by the lines.

Question 5

Theorem

Answer 5

Any translation or rotation is equivalent to a composition of two reflections