The point P (-1, 2) is rotated to become P’ (2, 1). describe the rotation by degree and direction.
A. -90 degree rotation
B. 180 degree rotation
C. 90 degree rotation
D. -270 degree rotation
To find the rotation, we need to find the angle and direction.
First, let's find the angle between the points P(-1, 2) and P'(2, 1). We can use the formula:
θ = arctan((y2-y1)/(x2-x1))
θ = arctan((1-2)/(2-(-1))) = arctan(-1/3)
Using a calculator, we find that θ ≈ -18.43 degrees.
The rotation angle is equal to the absolute value of this angle because it represents the rotation amount. Therefore, the rotation angle is approximately 18.43 degrees.
Next, let's determine the direction of rotation. To do this, we can consider the change in x and y coordinates.
In P(-1, 2), the x coordinate increases by 3 (from -1 to 2) and the y coordinate decreases by 1 (from 2 to 1). This indicates a clockwise rotation.
Therefore, the rotation is approximately 18.43 degrees clockwise.
Based on the given options, none of them match the rotation described. It's important to note that the rotation angle given in the options (-90, 180, 90, -270) are not consistent with the calculated angle of approximately 18.43 degrees.