Final answer:
Translation followed by reflection results in changing coordinate signs according to the axis of reflection after the shifting. Four possible transformations were analyzed, showing how each step affects the point's final position.
Step-by-step explanation:
When applying a transformation to a point in the form (x, y), the order of transformations is essential. Let's analyze each transformation step-by-step.
- Translation followed by reflection in the y-axis: A point (x, y) translated by (x, y - 1) becomes (x, y-1). When this point is then reflected in the y-axis, the x-coordinate changes sign, thus the new point becomes (-x, y-1).
- Translation followed by reflection in the y-axis: Starting with (x, y) and translating by (x, y + 1), we get (x, y+1). Reflecting this in the y-axis yields (-x, y+1).
- Translation followed by reflection in the x-axis: A point that has undergone translation (x, y - 1) is reflected in the x-axis, changing the sign of the y-coordinate to get (x, -y+1).
- Translation followed by reflection in the x-axis: After translating the point by (x, y + 1), reflection in the x-axis results in (x, -y-1).
Each combination of translation and reflection yields a distinct end point by altering the coordinates according to the transformation rules.