Question

Point A is at (-5,8). it is rotated about the origin and A' is at (8,5). How many degrees counterclockwise was A rotated (Just type the number).

a. 135 degrees
b. 45 degrees
c. 90 degrees
d. 180 degrees

Answer 1

The point A (-5,8) is rotated about the origin and becomes A' (8,5). The angle of rotation can be calculated using the arctangent function and is approximately 13.5°. The correct answer is (A) 135 degrees.

Step-by-step explanation:

The point A (-5,8) is rotated about the origin and becomes A' (8,5). We can calculate the angle of rotation by finding the difference in the coordinates.

First, let's calculate the difference in x-coordinates: 8 - (-5) = 13

Now, let's calculate the difference in y-coordinates: 5 - 8 = -3

Using these differences, we can calculate the angle using the arctangent function: atan(-3/13) ≈ -13.5°

Since the rotation is counterclockwise, the absolute value of the angle is 13.5°. Therefore, the correct answer is (A) 135 degrees.