Question

PLS HELP ASAP!!

Triangle XYZ is drawn with vertices at X(−1, −3), Y(−5, −5), Z(−4, −2). After a rotation, image X′Y′Z′ has vertices X′(3, −1), Y′(5, −5), Z′(2, −4).

Part A: Determine the two different rotations that would create the image. (1 point)

Part B: Explain how you know your answer to Part A is correct. (3 points)

Answer 1

To determine the rotations that would create the image, find the translation vector and the center of rotation.

Step-by-step explanation:

To determine the two different rotations that would create the image, we need to find the angle of rotation and the center of rotation. First, find the translation vector by subtracting the coordinates of the original point X from the coordinates of the new point X'. This gives us a translation vector (-1 - 3, 3 - (-1)) = (-4, 4).

Next, find the center of rotation by adding half of the x-coordinate of the translation vector to the x-coordinate of the original point X and subtracting half of the y-coordinate of the translation vector from the y-coordinate of the original point X. This gives us the center of rotation (-1 + (-4/2), -3 + (4/2)) = (-3, -1).