Question

recall that, in geometry, one type of rigid motion is a translation, or a \slide\. also recall that a function is a rule that assigns exactly one output to each input. the input to a function can be a point. a translation is a function, t, which takes as its input a set of pre - image points and outputs a set of image points. the pre - image points are translated a distance ab in the direction ab. when a figure is translated, the resulting figure is congruent to the original figure. consider pq perpendicular to cb. translate pq using the translation function t_tr(pq). first determine the direction and distance that pq will be translated. the function tells you that pq will be translated in the direction tr and the distance of tr. to translate pq, study the example and then answer each question. decide whether each statement about the example is true or false. pq is congruent to pq. pq is perpendicular to bc. pq is perpendicular to bc. m∠pp = m∠tr. m∠qq = m∠tr. tr || qq. the diagram below shows the function t_gk(sv). line gw is parallel to line segment sv. use the diagram to answer the remaining questions. complete the statement about the example. line segment pq was <in the direction> <a distance of>

Explanation:

Step1: Recall properties of translation

In a translation, the pre - image and the image are congruent, and corresponding line segments are parallel.

Step2: Analyze each statement

• For $\overline{TR}\parallel\overline{QQ'}$: In a translation, the vector representing the translation is parallel to the line segments connecting pre - image and image points of corresponding vertices. So this is True.
• For $m\angle PP'

eq m\angle TR$: Since translation is a rigid motion and preserves angle measures, and $\angle PP'$ and $\angle TR$ are not relevant in terms of angle - measure comparison in a translation context. But if we assume it's about some mis - written angle - related comparison, in a translation all angles in the pre - image and image are congruent. However, this statement's format seems off. If we consider it as a wrong comparison, it's False.

• For $m\angle QQ'

eq m\angle TR$: Similar to the above, wrong comparison, False.

• For $\overline{PQ}$ is perpendicular to $\overrightarrow{BC}$: Given that $\overline{PQ}$ is translated perpendicular to $\overrightarrow{CB}$, this is True as per the problem statement.
• For $\overline{PQ'}$ is congruent to $\overline{PQ}$: In a translation, pre - image and image line segments are congruent. So this is True.

Answer:

True, False, False, True, True