To find the coordinates of the new vertices \( X'Y'Z' \) after dilation with a center at the origin and a scale factor of 12, we will apply the dilation formula to each vertex.
Let’s denote the original coordinates of the vertices as:
- \( X(2, 4) \)
- \( Y(6, 0) \)
- \( Z(7, 2) \)
The formula for dilation with a scale factor \( k \) is given by:
\[ X' = k \cdot X \] \[ Y' = k \cdot Y \] \[ Z' = k \cdot Z \]
Substituting the scale factor \( k = 12 \):
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For vertex \( X(2, 4) \): \[ X' = (12 \cdot 2, 12 \cdot 4) = (24, 48) \]
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For vertex \( Y(6, 0) \): \[ Y' = (12 \cdot 6, 12 \cdot 0) = (72, 0) \]
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For vertex \( Z(7, 2) \): \[ Z' = (12 \cdot 7, 12 \cdot 2) = (84, 24) \]
Thus, the new coordinates after dilation are:
- \( X'(24, 48) \)
- \( Y'(72, 0) \)
- \( Z'(84, 24) \)
However, none of the provided options match these values exactly. Please check the original triangle coordinates or the scale factor if they were provided incorrectly in the question.
Based on the original vertices \( (2, 4), (6, 0), (7, 2) \), the correct new coordinates based on the calculations are \( X'(24, 48), Y'(72, 0), Z'(84, 24) \).
3 answers