Looking at the image, you have a set of three triangles on a coordinate grid. One of them is a rotation of triangle ABC, and the other is a reflection.

Let's solve the questions one by one:

1. Which triangle is the rotation of triangle ABC?

The rotation of triangle ABC will have the same orientation (no flipping) but rotated around a point.

• The green triangle, located in the second quadrant, maintains the same orientation as triangle ABC but appears rotated. It is likely a 90-degree counterclockwise rotation.

Answer: The green triangle is the rotation of triangle ABC.

a. What is the center of rotation?

• A 90-degree rotation typically occurs around the origin (0, 0). By checking the coordinates of the points, we can see that a 90-degree counterclockwise rotation of triangle ABC around the origin will match the location of the green triangle.

Answer: The center of rotation is the origin (0, 0).

2. Which triangle is the reflection of triangle ABC?

The reflection of triangle ABC will appear flipped, and the shape will be mirrored across an axis.

• The red triangle, located below the x-axis, is a mirror image of triangle ABC, indicating it is the reflection.

Answer: The red triangle is the reflection of triangle ABC.

a. Which axis is the line of reflection?

• Since triangle ABC and the red triangle appear mirrored across the x-axis (the horizontal line), the reflection occurs across the x-axis.

Answer: The line of reflection is the x-axis.

Would you like more details on how to perform geometric transformations? Here are 5 related questions to deepen your understanding:

1. How do you calculate the coordinates of a point after a 90-degree counterclockwise rotation around the origin?
2. What are the steps to reflect a point over the x-axis?
3. How do you determine the center of rotation for any given transformation?
4. How does a 180-degree rotation differ from a 90-degree rotation geometrically?
5. Can a reflection occur over an arbitrary line, like $y = x$? How does it change the coordinates?

Tip: Always check the orientation of triangles when identifying rotations or reflections; rotations preserve orientation, while reflections reverse it.