To perform a dilation with a scale factor of 2, centered at the origin, you need to multiply each coordinate of the vertices by the scale factor. In this case, the scale factor is 2.
Given the vertices:
- \( T = (-3, -4) \)
- \( U = (-3, -2) \)
- \( V = (-1, -2) \)
- \( W = (-1, -4) \)
Let's calculate the new coordinates after the dilation:
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For \( T' \): \[ T' = (2 \cdot -3, 2 \cdot -4) = (-6, -8) \]
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For \( U' \): \[ U' = (2 \cdot -3, 2 \cdot -2) = (-6, -4) \]
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For \( V' \): \[ V' = (2 \cdot -1, 2 \cdot -2) = (-2, -4) \]
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For \( W' \): \[ W' = (2 \cdot -1, 2 \cdot -4) = (-2, -8) \]
Thus, the coordinates of the vertices after the dilation are:
- \( T' = (-6, -8) \)
- \( U' = (-6, -4) \)
- \( V' = (-2, -4) \)
- \( W' = (-2, -8) \)
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