Question

Triangle A'B'C'is the image of triangle ABC under a rotation about the origin. (0,0)

determine the angle of rotation

a. -105
b. -75
c. 75
d. 105​

Answer 1

9514 1404 393

Answer:

b. -75°

Explanation:

Point A moves from (-4, -3) to (-4, 3). We can find the angle of rotation several ways. One is to consider the tangent of the angle relative to the x-axis.

Point A is on a line that makes an angle to the x-axis of ...

∠A = arctan(-3/-4) = 36.9°

Point A' is on a line that makes an angle to the x-axis of ...

∠A' = arctan(3/-4) = -36.9°

Then the change in angle is ...

∠A' -∠A = -36.9° -36.9° = -73.8°

The closest answer choice is ...

b. -75°