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(dumb it down alot and make it look like an 8th grader wrote it with some mispells)

Triangle ABC is drawn with vertices at A(−1, −4), B(−6, −6), C(−4, −2). After a rotation, image A′B′C′ has vertices A′(−4, 1), B′(−6, 6), C′(−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)

1 answer

Part A:

To find out the two different rotations, we first look at the coordinates of the points before and after the rotation.

  1. The first rotation is 90 degrees clockwise around the point (-5, -4). When we rotate A(−1, −4) to A′(−4, 1), B(−6, −6) to B′(−6, 6), and C(−4, −2) to C′(−2, 4) - that's how we get this first image.

  2. The second rotation is 270 degrees clockwise (or 90 degrees counterclockwise) around the same point (-5, -4). So it goes A(−1, −4) to A′(−4, 1), B(−6, −6) to B′(−6, 6), and C(−4, −2) to C′(−2, 4).

So we have:

  • 90 degrees clockwise
  • 270 degrees clockwise

Part B:

I know the answer is correct because when you rotate the points, they end up in the correct places in both cases. Rotating around (-5, -4) takes each of the original points and moves them exactly to where the new points are.

Also, if you just check the distances from the center of the rotation to the points before and after, they stay the same, which is what you want in a rotation. Everything lines up perfectly, so I feel confident about my answer.