data mining short question

State whether the following proximity measures—cosine, correlation, and Euclidean distance—are invariant (unchanged) under the following transformations. Specifically, if 𝑥→𝑥′ and 𝑦→𝑦′, would cosine(𝑥,𝑦) = cosine(𝑥′,𝑦′), correlation(𝑥,𝑦) = correlation(𝑥′,𝑦′), and Euclidean(𝑥,𝑦) = Euclidean(𝑥′,𝑦′). Please explain your answers by referring to the formula for each proximity measure. Simple yes or no would not be accepted.
I.Translation: 𝑥→𝑥 𝑐 and 𝑦→𝑦 𝑐, where 𝑐 is a constant added to each attribute value in 𝑥 and 𝑦.
II.Scaling: 𝑥→𝑐𝑥 and 𝑦→𝑐𝑦, where 𝑐 is a constant multiplied to each attribute value in 𝑥 and 𝑦.
III.Standardization: 𝑥→(x – c)/d and 𝑦→(y – c)/d where 𝑐 and 𝑑 are constants.