The point P(4, 2) is rotated to become P′(−2, 4) . Describe the rotation by degree and direction.(1 point) Responses −90° rotation (clockwise) negative 90 degrees rotation (clockwise) 180° rotation (counter clockwise) 180 degrees rotation (counter clockwise) 90° rotation (counter clockwise) 90 degrees rotation (counter clockwise) −270° rotation (clockwise) negative 270 degrees rotation (clockwise)

Answer 1

To find the degree and direction of the rotation from the point \( P(4, 2) \) to the point \( P'(-2, 4) \), we can analyze the coordinates.

1. Initial Point: \( P(4, 2) \)
2. Final Point: \( P'(-2, 4) \)

Steps to Determine the Rotation

1. Translate the Initial Point to the Origin:

   • For simplicity, we will consider the point in the standard position; we can imagine rotating it around the origin (0,0).

2. Relative Position:

   • The point \( P(4, 2) \) lies in the first quadrant.
   • The point \( P'(-2, 4) \) lies in the second quadrant.

3. Finding the Angle of Rotation:

   • The rotation can be visualized using the standard rotation degrees around the origin. Here, let's check the movement:
   • The original point is at \( (4, 2) \), which you can visualize as being slightly above the x-axis and to the right of the y-axis.
   • The new position \( (-2, 4) \) moves left into the second quadrant.

Rotation Calculation

To find the angle of rotation:

• When rotating \( P(4, 2) \) to \( P'(-2, 4) \), we can observe that:
  • Moving from \( (4, 2) \) to \( (0, 0) \), you essentially rotate from the positive x-axis.
  • To reach from the point in the first quadrant to the second quadrant, you would rotate 90 degrees counterclockwise.

Conclusion:

The point \( P(4, 2) \) is rotated to become \( P'(-2, 4) \) through a \( 90^\circ \) rotation counterclockwise.

Thus, the correct answer is:

90° rotation (counter clockwise)