To compare the side lengths of the original figure "mugwump" with the new figure obtained by applying the transformation \( (3X + 1, 3Y - 4) \), we need to analyze how the transformation affects the coordinates of the figure's vertices.
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Transformation Analysis:
- The transformation \( (X, Y) \rightarrow (3X + 1, 3Y - 4) \) involves scaling the \(X\) coordinate by a factor of 3 and translating it by adding 1, and scaling the \(Y\) coordinate by a factor of 3 and translating it by subtracting 4.
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Effect on Side Lengths:
- The scaling factor for both coordinates is 3. When the coordinates of a shape are scaled by a factor of \(k\), the lengths of the sides are scaled by that factor as well.
- Thus, every side length of the original figure (mugwump) will be multiplied by 3.
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Conclusion:
- The side lengths of the new figure will be 3 times the corresponding side lengths of the original figure.
In summary, if you apply the transformation \( (3X + 1, 3Y - 4) \) to the figure "mugwump," the side lengths of the new figure will be three times those of the original figure.
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