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:
-
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).
-
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).
-
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:
- 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'.
- Original A (-4, -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'.
- Original B (-3, -1):
- 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'.
- Original C (-1, -2):
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.
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