Subjects geometry

Scaled Copies 7Ed381

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Question: M1|L1 What Are Scaled Copies? Find a scaled copy of the original rectangle. To find which figure is a scaled copy, start by labeling the length and width of the original rectangle. Original Rectangle Top-center bracket over the original rectangle indicates the length; left-side bracket indicates the width; position_hint=top-right. Bottom-left large purple rectangle; position_hint=bottom-left. Bottom-right tall purple rectangle; position_hint=bottom-right.
1. **State the problem:** We need to find a scaled copy of the original rectangle. 2. **Label the original rectangle:** Let the length be $L$ and the width be $W$. 3. **Definition of scaled copy:** A scaled copy of a rectangle is another rectangle whose length and width are proportional to the original rectangle by the same scale factor $k$. 4. **Check the given rectangles:** - For the bottom-left large purple rectangle, measure or note its length $L_1$ and width $W_1$. - For the bottom-right tall purple rectangle, measure or note its length $L_2$ and width $W_2$. 5. **Calculate scale factors:** - Calculate $k_1 = \frac{L_1}{L}$ and $k_1' = \frac{W_1}{W}$. - Calculate $k_2 = \frac{L_2}{L}$ and $k_2' = \frac{W_2}{W}$. 6. **Determine which is a scaled copy:** - If $k_1 = k_1'$, then the bottom-left rectangle is a scaled copy. - If $k_2 = k_2'$, then the bottom-right rectangle is a scaled copy. 7. **Conclusion:** The rectangle whose length and width are scaled by the same factor $k$ compared to the original rectangle is the scaled copy. Since the problem does not provide numeric values, the method above is the way to identify the scaled copy.