Question

concept translations
a translation is a transformation in a plane
that maps all points of a preimage the same
distance and in the same direction.
the translation of \\( \triangle a b c \\) by \\( x \\) units along the
\\( x \\)-axis and by \\( y \\) units along the \\( y \\)-axis can be
written as \\( t _ { ( x , y ) } ( \triangle a b c ) = \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\).
a translation has the following properties:
if \\( t _ { ( x , y ) } ( \triangle a b c ) = \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\), then

• \\( \overline { a a ^ { \prime } } \parallel \overline { b b ^ { \prime } } \parallel \overline { c c ^ { \prime } } \\).
• \\( \overline { a a ^ { \prime } } \cong \overline { b b ^ { \prime } } \cong \overline { c c ^ { \prime } } \\).
• \\( \triangle a b c \\) and \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) have the same orientation.

a translation is a rigid motion, so length and angle measure are preserved.

1. select all that apply:

what does it mean to have the same
the same orientation?
\\( \square \\) same size
\\( \square \\) same shape
\\( \square \\) same direction
\\( \square \\) same location

Explanation:

Orientation in geometry means the arrangement of points relative to one another. When two figures have the same orientation, their corresponding parts are arranged in the same order. A translation (a type of rigid - motion) preserves the shape and size of a figure. Since length and angle measures are preserved (as translation is a rigid motion), the shape and size remain the same. The direction of individual points' movement (translation direction) is the same for all points in the pre - image to get the image, but this is about the translation vector, not the orientation in terms of shape - size - arrangement. And having the same location would mean no translation (or transformation) at all.

Answer:

same size, same shape