Question

1. fill in the statements below with \sometimes\, \always\ or

ever\ in order to make them true
a. a reflection will ________________ change the orientation of a figure.
b. a reflection will ________________ change the size of a figure.
c. a reflection will ________________ change the orientation of the vertices of the figure.

Explanation:

Part a

Step1: Recall reflection properties

A reflection is a transformation that flips a figure over a line (the line of reflection). By the definition of reflection, it is a rigid transformation that flips the figure, which changes the orientation (e.g., a clockwise - oriented figure may become counter - clockwise after reflection). So a reflection will always change the orientation of a figure.

Part b

Step1: Recall reflection properties

Reflection is a rigid transformation. Rigid transformations (reflection, rotation, translation) preserve the size (and shape) of the figure. So a reflection will never change the size of a figure.

Part c

Step1: Recall reflection properties

Since a reflection changes the orientation of the figure, and the vertices are part of the figure, the orientation of the vertices (the order in which they are arranged, e.g., clockwise or counter - clockwise order) will also be changed. So a reflection will always change the orientation of the vertices of the figure.

Answer:

s:
a. always
b. never
c. always