Show that the order in which transformations are performed is important by applying the transformations to the triangle A(1, 0), B(0, 1), C(1, 1) by i) rotating by 45 about the origin and then translating in the direction of the vector (1, 0) . ii) translating first and then rotating by 45 about the origin
Firstly, the transformations we'll be applying are rotation and translation. The rotation will be by 45 degrees about the origin, and the translation will be in the direction of the vector (1, 0).
### i) Rotate by 45 degrees about the origin and then translate in the direction of the vector (1, 0):
#### Step 1: Rotate the triangle by 45 degrees about the origin:
Let's denote the rotated vertices as A', B', and C'.
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