Question

What kind of a transformation, besides a translation, has been done to ΔABC
? a ( -5 , 4) b ( -2, 2) c ( 5, -1) a" (7,1) b"(4,-1) c"(3,2)

(1 point)
Responses

a composition
a composition

a rotation
a rotation

a rotation
a rotation

a reflection

Answer 1

To determine what kind of transformation has been applied to triangle ΔABC, we must analyze the coordinates of the points before and after the transformation.

Given the original points:
- A(-5, 4)
- B(-2, 2)
- C(5, -1)

And the transformed points:
- A'(7, 1)
- B'(4, -1)
- C'(3, 2)

1. **Translation**: We first check if the points can be related through a translation. If we compare the coordinates directly, we do not find a consistent shift pattern that can be applied to all points.

2. **Rotation**: We must determine if the original triangle can be rotated around a specific point to match the coordinates of the transformed triangle.

3. **Reflection**: A reflection would require that the distance from the reflection line to corresponding points is equal. Thus, we must check if the new points lie symmetrically with respect to a line.

By inspecting the points closely:

- A to A' appears to move in a manner that suggests neither simply reflecting nor rotating around the origin.
- Analyzing the coordinates individually for rotation reveals inconsistencies that would not support a clean 90-degree or 180-degree configuration.

Since the points A, B, and C do not translate uniformly nor do they align to suggest a direct rotational movement, the transformation appears to involve a reflection across a line or axis.

Ultimately, without specific calculations, the kind of transformation done to ΔABC that fits the evidence presented leans towards **a reflection**.

Thus, the correct response is:

**a reflection**.