Use the graph to answer the question.

Question

Graph of triangle ABC with vertices at negative 4 comma negative 4, 3 comma negative 3, 0 comma negative 10. A second triangle A prime, B prime C prime with vertices at 4 comma negative 4, 3 comma 3, 10 comma 0.

Determine the direction and degree of rotation used to create the image.
90° counterclockwise rotation
90° clockwise rotation
270° counterclockwise rotation
180° clockwise rotation

Answer 1

To determine the rotation that transforms triangle ABC into triangle A'B'C', we can analyze the vertices of both triangles.

Triangle ABC:

• A(-4, -4)
• B(3, -3)
• C(0, -10)

Triangle A'B'C':

• A'(4, -4)
• B'(3, 3)
• C'(10, 0)

The general rule for rotating points in the plane:

1. A 90° counterclockwise rotation would change point (x, y) to (-y, x).
2. A 90° clockwise rotation would change point (x, y) to (y, -x).
3. A 180° rotation would change point (x, y) to (-x, -y).

Let's analyze each vertex:

1. For point A (-4, -4):

   • After a 90° counterclockwise rotation, it would be (4, -4). This matches A' (4, -4).

2. For point B (3, -3):

   • After a 90° counterclockwise rotation, it would be (3, -3). This matches B' (3, 3) after changing signs (which indicates different vertices need to be checked).

3. For point C (0, -10):

   • After a 90° counterclockwise rotation, it would be (10, 0), which matches C' (10, 0).

From our vertex check:

• A transforms to A' correctly with a 90° counterclockwise rotation.
• B does not match directly, so instead, let's check subsequent transformations.

After re-examining: When applying the rotation, it seems that triangle ABC transforms similarly under 180° rotation where each coordinate would go to its opposite.

Final Conclusion: The transformation that correctly aligns vertices of triangle ABC to triangle A'B'C' is a 180° clockwise rotation.