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English has contractions in many cases because we have a system of weak and strong vowels, based on where the stress falls in the sentence. "That's" arose because the vowel sound in the non-stressed "is" has weakened to the point that it goes essentially unpronounced next to the strong /æ/ of "That." In the case of "This is," both share the same weak vowel sound, so "is" doesn't get contracted in, as it doesn't lose the vowel per se, though it does persist in its reduced, nearly absent form.
This is (name)". Eu expliquei a ela que não conhecia essa contração (short form) e que não sabia se era correta.
Porém ela respondeu que a professora da escola regular ensinou daquela forma e que era certo.
The reason we don't contract it in writing is because we don't contract it in speaking.