Question

The vertices of a rectangle are M(-5,-5), N(-1,-5), O(-1,1), and P(-5,1). A rotation about the origin maps P'to the point (1,5). The rotation was _degrees.

Option 1: 90° counterclockwise
Option 2: 180° counterclockwise
Option 3: 270° clockwise
Option 4: 180° clockwise

Answer 1

The rotation that maps P to the point (1,5) with the vertices of the rectangle given is a 90° counterclockwise rotation around the origin, consistent with standard polar coordinates.

Step-by-step explanation:

The vertices of a rectangle are M(-5,-5), N(-1,-5), O(-1,1), and P(-5,1). A rotation about the origin maps P to the point (1,5). To determine the degree of rotation, consider the initial position of P and its final position after the rotation. The point P started at (-5, 1) and ended at (1, 5).

By analyzing the change in coordinates, we can see that the x-value changed from -5 to 1, and the y-value changed from 1 to 5. This indicates a 90° counterclockwise rotation when following the standard polar coordinates convention, where the positive direction of angles is counterclockwise and the negative direction is clockwise. Therefore, the correct answer is Option 1: 90° counterclockwise.