Answer the following questions on the effect of coordinate transformations on the area of a triangle.
a. (i) Explain, with reason, whether the area of a triangle changes when each of its vertices is translated by the same vector.
b. (ii) A student claims that multiplying the x- and y-coordinates of every vertex by the same factor k will leave the area unchanged because the shape of the triangle appears similar. Do you agree? Justify your answer and illustrate with a numerical example.
c. (iii) Identify one practical situation in surveying or cartography where understanding the difference between translation and scaling of coordinates is important, and briefly describe why.