the point P (-1,2) is rotated to become P' (2,1). Describe the rotation by degree and direction.

Question

a. -270 rotation
b. 180 rotation
c. 90 rotation
d. -90 rotation

Answer 1

To determine the rotation that takes point $P(-1,2)$ to point $P^{\prime }(2,1)$, we can analyze the change in coordinates.

1. Original Point $P(-1,2)$:

   • $x=-1$
   • $y=2$

2. New Point $P^{\prime }(2,1)$:

   • $x^{\prime }=2$
   • $y^{\prime }=1$

Calculation of Rotation:

We can use the following transformation formulas to investigate the effect of various rotations on the coordinates.

• A 90-degree rotation counterclockwise about the origin transforms $(x,y)$ to $(-y,x)$.
• A 90-degree rotation clockwise (or -90 degrees counterclockwise) transforms $(x,y)$ to $(y,-x)$.
• A 180-degree rotation transforms $(x,y)$ to $(-x,-y)$.
• A 270-degree rotation counterclockwise (or -90 degrees clockwise) transforms $(x,y)$ to $(y,-x)$.

Checking Each Option:

1. Option a: -270 degrees (equivalently 90 degrees clockwise)

   • $(-1,2)\to (2,1)$ (Correct)

2. Option b: 180 degrees

   • $(-1,2)\to (1,-2)$ (Incorrect)

3. Option c: 90 degrees

   • $(-1,2)\to (-2,-1)$ (Incorrect)

4. Option d: -90 degrees

   • $(-1,2)\to (2,-1)$ (Incorrect)

Given the calculations, the rotation that takes point $P(-1,2)$ to point $P^{\prime }(2,1)$ is a -270 degree rotation (or 90 degrees clockwise).

Conclusion:

The correct answer is: a. -270 rotation