To find the coordinates of the vertices \( A', B', C', \) and \( D' \) after performing a dilation with a scale factor of 3 centered at the origin, you multiply the coordinates of each vertex by the scale factor.
The coordinates of the original vertices are:
- \( A(-5, 1) \)
- \( B(-2, 1) \)
- \( C(-2, 6) \)
- \( D(-5, 6) \)
Let's calculate the coordinates after the dilation:
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For point \( A' \): \[ A' = (3 \times -5, 3 \times 1) = (-15, 3) \]
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For point \( B' \): \[ B' = (3 \times -2, 3 \times 1) = (-6, 3) \]
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For point \( C' \): \[ C' = (3 \times -2, 3 \times 6) = (-6, 18) \]
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For point \( D' \): \[ D' = (3 \times -5, 3 \times 6) = (-15, 18) \]
Thus, the coordinates of the dilated points are:
- \( A'(-15, 3) \)
- \( B'(-6, 3) \)
- \( C'(-6, 18) \)
- \( D'(-15, 18) \)
The correct response is: A′(−15, 3), B′(−6, 3), C′(−6, 18), and D′(−15, 18).