Question

Point A(-3, -3) is rotated counterclockwise about the origin so that A^1 = (3, -3). Find the angle of rotation.

The angle of rotation is how many degrees?
A) 90 degrees
B) 180 degrees
C) 270 degrees
D) 360 degrees

Answer 1

The angle of rotation between point A(-3, -3) and its counterclockwise rotated position is 0 degrees.

Step-by-step explanation:

The angle of rotation can be found by finding the angle between the original point A(-3, -3) and the rotated point A^1(3, -3).

To find the angle between two points, we can use the inverse tangent function.

Let's call the angle of rotation x.

Using the inverse tangent function, we have: tan(x) = (A^1_y - A_y) / (A^1_x - A_x).

Plugging in the values, we have: tan(x) = (-3 - (-3)) / (3 - (-3)).

Simplifying, we get: tan(x) = 0 / 6 = 0.

Since tangent is 0 at 0 degrees and all multiples of 180 degrees, the angle of rotation is 0 degrees.