To dilate a point \( (x, y) \) around the origin with a scale factor of \( k \), you can use the formula:
\[ (x', y') = (kx, ky) \]
In this case, the scale factor \( k \) is 2.
Let's find the new vertices \( A', B', C', \) and \( D' \) using the given coordinates:
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Point A (-3, 3): \[ A' = (2 \times -3, 2 \times 3) = (-6, 6) \]
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Point B (1, 5): \[ B' = (2 \times 1, 2 \times 5) = (2, 10) \]
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Point C (4, -1): \[ C' = (2 \times 4, 2 \times -1) = (8, -2) \]
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Point D (1, -5): \[ D' = (2 \times 1, 2 \times -5) = (2, -10) \]
Now, we have the new vertices:
- \( A'(-6, 6) \)
- \( B'(2, 10) \)
- \( C'(8, -2) \)
- \( D'(2, -10) \)
Looking at the answer choices provided, the correct transformed vertices are:
A'(-6, 6), B'(2, 10), C'(8, -2), and D'(2, -10).
So the correct answer is: A'(-6, 6), B'(2, 10), C'(8, -2), and D'(2, -10).