Question

which statement is false?
a uv = uv
b uv = uv
c uu = uu
d uu = vv

Explanation:

Step1: Recall the properties of translation

Translation is a transformation that moves every point of a figure or space by the same distance in a given direction. So, \(UV = U'V'\) (because \(U'V'\) is the translation of \(UV\) along line \(k\)), and \(UV=U''V''\) (because \(U''V''\) is the translation of \(UV\) along line \(m\)). Also, since the translation distance along line \(k\) and line \(m\) is the same (as it is a translation of the same segment \(UV\) in different parallel directions), \(UU' = VV'\) and \(UU''=VV''\).

Step2: Analyze each option

• Option A: \(UV = U'V'\) is True because of the property of translation.
• Option B: \(UV = U''V''\) is True because of the property of translation.
• Option C: \(UU'

eq UU''\) because \(UU'\) is the translation distance along line \(k\) and \(UU''\) is the translation distance along line \(m\) (different paths of translation).

• Option D: \(UU'' = VV''\) is True because in translation, the distance of translation for corresponding points is the same.

Answer:

C. \(UU'=UU''\)