Triangle ABC has vertices A(1,2), B(4,3) and C(2,7). Answer the following.
(i) Find the area of △ABC. Write your answer in exact form.
(ii) The triangle is translated so that each vertex is moved by the vector (5,−2). Calculate the area of the translated triangle A′B′C′ and compare it with the area obtained in part (i).
(iii) Starting again from the original triangle ABC, every coordinate is multiplied by 3 while keeping the origin fixed. Determine the area of the new triangle A′′B′′C′′ and express it as a multiple of the area found in part (i).
(iv) From the numerical results of parts (i)–(iii), state a general conclusion about how (a) a translation and (b) a uniform scaling by a factor k affect the area of any triangle given by its vertices.