Answer:
The most important characteristics of a translation are:
1. It preserves the shape and size of the original figure.
2. Every point of the original figure moves the same distance in the same direction to form the new figure.
3. The orientation of the original figure remains the same.
The steps of the construction connect to these characteristics as follows:
1. Choose a vector (a, b) which will determine the distance and direction of the translation.
2. Label the coordinates of each point in the original figure.
3. Apply the vector (a, b) to each point in the original figure to find the corresponding point in the new figure.
4. Plot the new points to form the translated figure.
Step 1 establishes the distance and direction of the translation, which ensures that the size and shape of the original figure are preserved in the new figure. This corresponds to characteristic 1.
Step 3 involves applying the same vector to each point, which ensures that each point moves the same distance in the same direction, preserving the relative positions of the points in the original figure. This corresponds to characteristic 2.
Finally, since the orientation of the original figure remains the same, the new figure will have the same orientation as the original. This corresponds to characteristic 3.
Explanation: