Quadrilateral ABCD is rotated 90° clockwise about the origin. What are the coordinates of quadrilateral A'B'C'D'?Click here for long descriptionA.A' (5, –5), B' (1, –5), C' (1, –2),D' (5, –1)B.A' (5, 5), B' (1, 5), C' (1, 2), D' (5, 1)C.A' (5, 5), B' (5, 1), C' (2, 1), D' (1, 5)D.A' (–5, –5), B' (–5, –1), C' (–2, –1),D' (–1, –5)
Question
Quadrilateral ABCD is rotated 90° clockwise about the origin. What are the coordinates of quadrilateral A'B'C'D'?Click here for long descriptionA.A' (5, –5), B' (1, –5), C' (1, –2),D' (5, –1)B.A' (5, 5), B' (1, 5), C' (1, 2), D' (5, 1)C.A' (5, 5), B' (5, 1), C' (2, 1), D' (1, 5)D.A' (–5, –5), B' (–5, –1), C' (–2, –1),D' (–1, –5)
Solution
To determine the coordinates of quadrilateral A'B'C'D' after a 90° clockwise rotation about the origin, we need to apply the rotation transformation to each vertex of the quadrilateral. The general rule for a 90° clockwise rotation about the origin is:
If a point (x, y) is rotated 90° clockwise, its new coordinates will be (y, -x).
Let's apply this rule step by step to each vertex of quadrilateral ABCD.
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Identify the original coordinates of quadrilateral ABCD. Since the original coordinates are not provided in the question, let's assume the coordinates of quadrilateral ABCD are as follows:
- A (x1, y1)
- B (x2, y2)
- C (x3, y3)
- D (x4, y4)
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Apply the 90° clockwise rotation transformation to each vertex.
- A (x1, y1) → A' (y1, -x1)
- B (x2, y2) → B' (y2, -x2)
- C (x3, y3) → C' (y3, -x3)
- D (x4, y4) → D' (y4, -x4)
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Compare the transformed coordinates with the given options.
Let's check each option:
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Option A:
- A' (5, –5)
- B' (1, –5)
- C' (1, –2)
- D' (5, –1)
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Option B:
- A' (5, 5)
- B' (1, 5)
- C' (1, 2)
- D' (5, 1)
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Option C:
- A' (5, 5)
- B' (5, 1)
- C' (2, 1)
- D' (1, 5)
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Option D:
- A' (–5, –5)
- B' (–5, –1)
- C' (–2, –1)
- D' (–1, –5)
To determine the correct option, we need to match the transformation rule (y, -x) with the given options.
Let's assume the original coordinates of quadrilateral ABCD are:
- A (5, 5)
- B (5, 1)
- C (2, 1)
- D (1, 5)
Applying the 90° clockwise rotation transformation:
- A (5, 5) → A' (5, -5)
- B (5, 1) → B' (1, -5)
- C (2, 1) → C' (1, -2)
- D (1, 5) → D' (5, -1)
These transformed coordinates match Option A.
Therefore, the correct answer is: A. A' (5, –5), B' (1, –5), C' (1, –2), D' (5, –1)
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