Question

Describe the transformation in the diagram.
B (-3, -1) A (-4, -2) C (-1, -2)
B' (1, -3) A' (2, -4) C' (2, -1)
A. 90 degrees clockwise rotation about the origin
B. 90 degrees counterclockwise rotation about the origin
C. 270 degrees counterclockwise rotation about the origin
D. 180 degrees counterclockwise rotation about the origin

Answer 1

To determine the transformation between the points A, B, C and their transformed points A', B', C', we will analyze each point.

The original points are:
- A (-4, -2)
- B (-3, -1)
- C (-1, -2)

The transformed points are:
- A' (2, -4)
- B' (1, -3)
- C' (2, -1)

### Analysis of transformation:
1. **Point A (-4, -2) to A' (2, -4):**
- The transformation involves changes in coordinates:
- The x-coordinate changes from -4 to 2 (a change of +6).
- The y-coordinate changes from -2 to -4 (a change of -2).

2. **Point B (-3, -1) to B' (1, -3):**
- The x-coordinate changes from -3 to 1 (a change of +4).
- The y-coordinate changes from -1 to -3 (a change of -2).

3. **Point C (-1, -2) to C' (2, -1):**
- The x-coordinate changes from -1 to 2 (a change of +3).
- The y-coordinate changes from -2 to -1 (a change of +1).

### Determine Transformation Type:
To check the possibility of 90 degrees rotation:
- A point (x, y) after a 90 degrees clockwise rotation about the origin transforms to (y, -x).
- A point (x, y) after a 90 degrees counterclockwise rotation about the origin transforms to (-y, x).

Now, let’s analyze:
1. For A:
- Original A (-4, -2):
- For 90 degrees clockwise: A would move to (-2, 4) — this is not A'.
- For 90 degrees counterclockwise: A would move to (2, -4) — this matches A'.
2. For B:
- Original B (-3, -1):
- For 90 degrees clockwise: B would move to (-1, 3) — this does not match B'.
- For 90 degrees counterclockwise: B would move to (1, -3) — this matches B'.
3. For C:
- Original C (-1, -2):
- For 90 degrees clockwise: C would move to (-2, 1) — this does not match C'.
- For 90 degrees counterclockwise: C would move to (2, -1) — this matches C'.

Since all original points match their transformed counterparts consistently only for a **90 degrees counterclockwise rotation**, the transformation described in the diagram is:

**Answer: B. 90 degrees counterclockwise rotation about the origin.**