Final answer:
The transformation (x, y) --> (8x, 4y) represents a similarity transformation because it changes the size of the shape. Vectors can form right-angle triangles with their components, and the Pythagorean theorem is used to calculate the resultant vector when two vectors are at right angles. Displacement is the same regardless of the path taken if the end point is the same, and a position vs time graph for an accelerating object is not a straight line.
Step-by-step explanation:
Addressing the student's question regarding whether the transformation (x, y) --> (8x, 4y) represents a similarity transformation but not a congruent transformation, the answer is True. A similarity transformation involves changing the size of a shape without altering its shape, which means it’s scaled by a factor. Since the x-coordinate is multiplied by a different factor than the y-coordinate, the shape will be distorted, and hence, it's not a congruent transformation.
In relation to vector operations, and understanding the displacement in vectors, it is True that a vector can form the shape of a right-angle triangle with its x and y components. This is because vectors can be broken down into perpendicular components, and these components can be viewed as the sides of a right-angle triangle.