Question

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

Answer 1

To describe the rotation that occurred, we need to find the angle and direction of rotation.

First, let's plot the points P(-1, 2) and P'(2, 1) on a coordinate system.

P is located at (-1, 2) and P' is located at (2, 1).

Now, to find the angle and direction of rotation, we can use the formula:

θ = arctan((y2 - y1) / (x2 - x1))

where (x1, y1) are the coordinates of P and (x2, y2) are the coordinates of P'.

Using the formula, we get:

θ = arctan((1 - 2) / (2 - (-1)))
= arctan(-1 / 3)
≈ -18.43 degrees

So, the angle of rotation is approximately -18.43 degrees.

To determine the direction of rotation, we can observe the movement of the points on the coordinate system.

In this case, P' is rotated counterclockwise from P. Therefore, the direction of rotation is counterclockwise.

In summary, the rotation is by approximately -18.43 degrees counterclockwise.