how would you describe the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II to show that the rectangles are congruent
To move the rectangle in Quadrant IV to the rectangle in Quadrant II and demonstrate congruence, the following series of transformations could have occurred:
1. Translation: The rectangle in Quadrant IV is horizontally shifted to the left across the x-axis by a certain distance.
2. Reflection: The translated rectangle is then reflected across the y-axis, creating an image in Quadrant II.
3. Rotation: The reflected rectangle is rotated about the origin (0,0) in a counterclockwise direction by 180 degrees.
These three transformations guarantee that the rectangles in Quadrant IV and Quadrant II are congruent, as they preserve shape and size.