Question

Use the image to answer the question.

Two triangles are drawn on a coordinate plane. Triangle A (-4,-2) B (-3,-1) C (-1,-2) is drawn with a solid line and is in quadrant 3. Triangle A prime (2,-4) B prime (1,-3) C prime (2, -1) is drawn with a dotted line and is in quadrant 4.

Describe the transformation in the diagram.

(1 point)
Responses

270° counterclockwise rotation about the origin
270 degrees counterclockwise rotation about the origin

180° counterclockwise rotation about the origin
180 degrees counterclockwise rotation about the origin

90° clockwise rotation about the origin
90 degrees clockwise rotation about the origin

90° counterclockwise rotation about the origin
90 degrees counterclockwise rotation about the origin
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Answer 1

To determine the transformation from triangle A (-4, -2) B (-3, -1) C (-1, -2) to triangle A' (2, -4) B' (1, -3) C' (2, -1), we can analyze the coordinates of the points and evaluate possible rotations.

Let's start with the coordinates of triangle A:
- A (-4, -2)
- B (-3, -1)
- C (-1, -2)

Next, let's look at the coordinates of triangle A':
- A' (2, -4)
- B' (1, -3)
- C' (2, -1)

Now we can examine the effects of the given transformations:

1. **90° clockwise rotation about the origin**: This transformation takes a point (x, y) to (y, -x).
2. **90° counterclockwise rotation about the origin**: This transformation takes a point (x, y) to (-y, x).
3. **180° counterclockwise rotation about the origin**: This transformation takes a point (x, y) to (-x, -y).
4. **270° counterclockwise rotation about the origin**: This transformation takes a point (x, y) to (y, -x).

Now, let's apply the 90° clockwise rotation to triangle A:

- A (-4, -2) → A' (y, -x) = (-2, 4) (not matching)
- B (-3, -1) → B' (y, -x) = (-1, 3) (not matching)
- C (-1, -2) → C' (y, -x) = (-2, 1) (not matching)

Next, applying the 90° counterclockwise rotation:

- A (-4, -2) → A' (-(-2), -4) = (2, -4) (matching)
- B (-3, -1) → B' (-(-1), -3) = (1, -3) (matching)
- C (-1, -2) → C' (-(-2), -1) = (2, -1) (matching)

So, the points do match under the 90° counterclockwise rotation.

Thus, the transformation is:
**90° counterclockwise rotation about the origin**.