Short Answer 
The quadrilateral PQRS is rotated 90 degrees clockwise around the origin, transforming point P from coordinates (-1, -2) to P’ at (2, 1). The new y-coordinate for P’ after rotation is confirmed to be 1, demonstrating the significant change in the shape’s orientation on the y-axis.
Step 1: Understand the Rotation Process
To comprehend how quadrilateral PQRS transforms into P’Q’R’S’ through rotation, it’s vital to know that we are rotating the shape 90 degrees clockwise around the origin (0,0), referred to as “O.” This means that every point on the quadrilateral will be moved in a circular direction towards the right. By applying specific mathematical transformations, we will determine the new coordinates.
Step 2: Apply the Rotation Formula
Utilizing the rotation transformation for a point (x, y), after a 90-degree clockwise rotation, the formula to determine the new coordinates P’ becomes P’ = (y, -x). For example, point P with coordinates (-1, -2) can be transformed. Implementing the formula yields:
- P’ = (-2, 1)
Thus, the new y-coordinate for point P’ after the rotation is now clearly 1.
Step 3: Conclusion and Result Interpretation
In conclusion, after performing a 90-degree clockwise rotation, the coordinates of point P change from (-1, -2) to P’ at (2, 1). Therefore, regarding the y-ordinate of the rotated point P’, it is confirmed to be 1. This indicates that point P’ is now located significantly higher on the y-axis, showcasing the drastic effects of the rotation on the shape’s orientation.