Question

translations
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 ( overline{pq} ) perpendicular to ( overrightarrow{cb} ). translate ( overline{pq} ) using the translation
function ( t_{tr}(overline{pq}) )
study the example and then answer each question.
decide whether each statement about the example is true
true false ( overline{pq} ) is congruent to ( overline{pq} ).
true false ( overline{pq} ) is perpendicular to ( overrightarrow{bc} ).
true false ( moverline{qq}
eq moverline{tr} )
true false ( moverline{pp}
eq moverline{tr} )
true false ( overrightarrow{tr}paralleloverrightarrow{qq} )
complete the statement about the example. line segment

Explanation:

Step1: Properties of translation

Translation is a rigid motion. In rigid motion, the length of the line - segment remains the same. So, if \(PQ\) is translated to \(P'Q'\), then \(P'Q'\cong PQ\) (True).

Step2: Direction of translation and perpendicularity

Since \(PQ\) is translated along \(TR\) (assuming \(TR\) is the direction of translation). If \(PQ\perp CB\), and translation is a slide (no rotation in the sense of changing the perpendicular relationship with a fixed line \(CB\) if \(TR\) is parallel to the direction of translation which does not affect the perpendicularity. \(PQ\) and \(P'Q'\) are parallel (because of translation), and if \(PQ\perp CB\), then \(P'Q'\perp CB\). But we need to check the relationship between \(PQ\) and \(BC\) (assuming a typo in the problem, if \(PQ\) is perpendicular to \(CB\) and translation is along \(TR\) (a non - perpendicular direction to \(CB\)), \(PQ\) is not perpendicular to \(BC\) (False).

Step3: Lengths in translation

In a translation, the distance of translation for all points of the pre - image is the same. If \(PQ\) is translated by the vector \(TR\), then \(QQ' = TR\) (so \(m\overline{QQ'}=m\overline{TR}\), False).

Step4: Lengths in translation

Since \(PP'\) and \(TR\) are both vectors of translation (assuming the translation is by the vector \(TR\)), \(m\overline{PP'}=m\overline{TR}\) (False).

Step5: Parallelism in translation

Since \(PP'\) and \(QQ'\) are both vectors of translation (assuming the translation is by the vector \(TR\)), \(TR\parallel QQ'\) (True).

Answer:

True, False, False, False, True