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:
- 90° clockwise rotation about the origin: This transformation takes a point (x, y) to (y, -x).
- 90° counterclockwise rotation about the origin: This transformation takes a point (x, y) to (-y, x).
- 180° counterclockwise rotation about the origin: This transformation takes a point (x, y) to (-x, -y).
- 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.
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